What is entanglement, both classical and quantum and what is the difference between these ?

[b_alsept@alsept]

I realize Bell's theorem sets mathematical limits on two particles that are correlated by polarization only but particles have properties other than polarization.

For example what about two particles that are perfectly correlated in speed, direction, polarization and rotating or pulsating at the same RPM or frequency. Now the measurements would become linear dependent. Bell's theorem wouldn't apply in that situation.

[swansont]

8 hours ago, b_alsept@alsept said:

I realize Bell's theorem sets mathematical limits on two particles that are correlated by polarization only but particles have properties other than polarization.

For example what about two particles that are perfectly correlated in speed, direction, polarization and rotating or pulsating at the same RPM or frequency. Now the measurements would become linear dependent. Bell's theorem wouldn't apply in that situation.

If you could entangle these properties it would apply, but you would have to formulate it in an appropriate fashion.

Not all correlations imply entanglement. If a particle at rest alpha decays, for example, there us a correlation between the kinetic energy of daughter and alpha, But there is no entanglement, as these KE values are known.

[Markus Hanke]

I must admit I’m confused about the last few comments. Entanglement is a correlation between measurement outcomes, in the sense that the multi-partite system is non-separable. Knowing whether a system is entangled requires one to take measurements on all parts, and then bring the results together and compare them.

The only thing special about quantum entanglement is that the correlation is stronger than classically allowed.

[swansont]

2 hours ago, Markus Hanke said:

The only thing special about quantum entanglement is that the correlation is stronger than classically allowed.

I disagree. If I have a left glove and a right glove, they are correlated 100%, and you can’t get stronger than that. One special component of entanglement is that the states are undetermined until measured, not just hidden from observation.

 

[studiot]

8 minutes ago, swansont said:

I disagree. If I have a left glove and a right glove, they are correlated 100%, and you can’t get stronger than that. One special component of entanglement is that the states are undetermined until measured, not just hidden from observation.

Not sure how this plays out with you previous statement or my 'coloured balls in a bag' example.

What if someone blind selected two gloves from a pile of gloves ?

How would they be classically entangled unless you had the 'extra information' ( my version of your words I think)  that they were a pair  ?

23 hours ago, swansont said:

If you have entangled spins the spins are correlated, but undetermined before measurement. e.g. if you measure an electron spin up, you know its entangled partner is spin down, but they did not have those spins prior to the measurement, unlike in a classical correlated system.

Edited October 30, 2021 by studiot

[swansont]

1 hour ago, studiot said:

Not sure how this plays out with you previous statement or my 'coloured balls in a bag' example.

What if someone blind selected two gloves from a pile of gloves ?

How would they be classically entangled unless you had the 'extra information' ( my version of your words I think)  that they were a pair  ?

Pulling random gloves from a pile (or balls from a bag) is a straight probability calculation. The glove’s handedness is determined even if not known. 

My point was that there are limitations to saying the correlation is higher in quantum systems; it’s true in a Bell’s inequality experiment. It’s a case of classical physics not explaining the degree of correlation. But the underlying behavior is quantum - measuring a spin or polarization is not the same as determining the handedness of a glove. There’s no glove measurement analogue to putting the polarizers at 0 degrees and 45 degrees for photons.

[studiot]

2 hours ago, swansont said:

Pulling random gloves from a pile (or balls from a bag) is a straight probability calculation. The glove’s handedness is determined even if not known. 

My point was that there are limitations to saying the correlation is higher in quantum systems; it’s true in a Bell’s inequality experiment. It’s a case of classical physics not explaining the degree of correlation. But the underlying behavior is quantum - measuring a spin or polarization is not the same as determining the handedness of a glove. There’s no glove measurement analogue to putting the polarizers at 0 degrees and 45 degrees for photons.

I don't think you caught my drift.

With the balls, determining the colour of one ball could tell you  absolutely nothing about the colour of the other.

Further you can't determine probabilities without further information.

[swansont]

48 minutes ago, studiot said:

I don't think you caught my drift.

With the balls, determining the colour of one ball could tell you  absolutely nothing about the colour of the other.

Further you can't determine probabilities without further information.

I guess not. I don’t see a connection. There is no “classical entanglement” (if there is such a thing) in your example. With spin or polarization, you know the two possible outcomes, and know how they must relate to each other. So this “further information” is available.

[b_alsept@alsept]

8 hours ago, swansont said:

If you could entangle these properties it would apply, but you would have to formulate it in an appropriate fashion.

I'm talking about physically correlating two particles and sending them off to be tested later. Just by adding frequency which also adds linear dependency you can test millions of these correlated pairs (not entangled) so that the results will produce all the predictions of QM, matching Malus Law or cos2theta.

[swansont]

5 hours ago, b_alsept@alsept said:

I'm talking about physically correlating two particles and sending them off to be tested later. Just by adding frequency which also adds linear dependency you can test millions of these correlated pairs (not entangled) so that the results will produce all the predictions of QM, matching Malus Law or cos2theta.

You need to explain how the properties are entangled

[b_alsept@alsept]

1 hour ago, swansont said:

You need to explain how the properties are entangled

They are intentionally correlated.

[Bufofrog]

25 minutes ago, b_alsept@alsept said:

They are intentionally correlated.

I think he is looking for a tad more detail.

[b_alsept@alsept]

7 hours ago, swansont said:

You need to explain how the properties are entangled

To explain something at the atomic level would take a lot more time and space than we have here, but it can be done. Because you asked, I'll show how adding a time dependent property to a particle, totally changes the probability of it passing a slit. You'll see it matches QM predictions.

Malus Law or cos2theta is found just about everywhere in QM, including one simple experiment where particles are sent through multiple polarizers set at different angles. I realize this is not the double slit experiment but it does explain the effect that a time dependent property has on the chances of a particle making it through a slit.

Instead of photons or electrons I'll use larger objects to help demonstrate this. Of course testing one particle/object would not be enough. I’m talking about testing thousands, at multiple set points. I could choose from hundreds of different objects but to be analogous and to make a point, let’s say the objects are 30cm-long throwing knives, 40mm tall and 5mm thick.

Their properties include a few things such as: (1) Every knife is moving at the same speed and will reach the tester at the same time. (2) As they move toward the tester, they each rotate vertically end over end at the same RPM. (3) The tester/analyzers is a wall, with a 39mm wide slots which can be rotated to different set points ranging from vertical to horizontal. The knives are not in phase with some rotating to different angles when they reach the tester.

When the slot is set to vertical, all knives will pass through but when the slot is set to horizontal, no knife can pass. If you rotate the slot five degrees from vertical, most of the knife's will still make it through but there's a slim chance the rotating knife will make contact with one of the slots edges. With the slot set vertically, all knives make it through, but at five degrees it’s obvious that the odds have been slightly reduced.

When you set the slot to 25 degrees from vertical it becomes harder for a knife to pass through, but you can see that if the knife is rotated just right as it reaches the slot, it will. If the set point is at 85 degrees (not quite horizontal), then most likely the knife will not make it through but there's still a very slim chance that if the knife is pointed at the slot as it gets there, it will pass.

After throwing thousands of vertically rotating/polarized knives at various set points ranging from vertical to horizontal you accumulate the results. The results will show that the number of knives passing through the slot is directly proportionate to the set point angle. More interesting is that the proportional results are NOT LINEAR. Instead you’ll find that they match Malus Law and cos2theta.

Adding a rotation, pulse or some kind of oscillation (which would explain frequency) will explain how correlation (not entanglement) produces the interference patterns. we observe.

 

[studiot]

16 hours ago, swansont said:

I guess not. I don’t see a connection. There is no “classical entanglement” (if there is such a thing) in your example. With spin or polarization, you know the two possible outcomes, and know how they must relate to each other. So this “further information” is available.

What are you expecting a connection between ?

As far as I can see we have the following situation.

1.  Two particles can be 'entangled' if they have a binary property ie that can be measured in one of two states.

OOps the daft control functions got me again before I had finished typing and posted this prematurely.

Edited October 31, 2021 by studiot

[Markus Hanke]

21 hours ago, swansont said:

I disagree. If I have a left glove and a right glove, they are correlated 100%, and you can’t get stronger than that. One special component of entanglement is that the states are undetermined until measured, not just hidden from observation.

Yes, of course. But what I meant here isn’t the maximum correlation (which is always 1 of course), but how it is distributed as a function of detector angle in the classical Bell experiment (graph taken from Wiki). You can see the quantum correlation is stronger than classical correlation (local realism):

[studiot]

3 minutes ago, studiot said:

16 hours ago, swansont said:

I guess not. I don’t see a connection. There is no “classical entanglement” (if there is such a thing) in your example. With spin or polarization, you know the two possible outcomes, and know how they must relate to each other. So this “further information” is available.

 

What are you expecting as a connection between ?

As far as I can see we have the following situation.

1.  Two particles can be 'entangled' if they have a binary property ie that can be measured in one of two states.
   For example a ball can be red or blue, an electron can be spin up or spin down etc.
    
2.  Note I have said 'can be entangled' because that is not enough. To actually cause entanglement something extra has to happen to the particles.
   For instance the two balls can be placed into a bag. The two electrons can be bonded in a bonding orbital.
   In the case of the balls we also have to ensure that one blue and one red have been selected. In the case of the electrons this step is not necessary as it will happen automatically on bonding.
    
3.  Another difference is that balls in general can come in many different colours so we have to restrict them. Electrons can only come in one of two spin states.
    
4. Entanglement can occur irrespective of our knowledge of these states, for both the balls and the electrons.
    
5. We can know that the bonded electrons are entangled without knowing which has which spin.
   Measuring one spin will automatically determine the other.
   We can only know the balls are entangled if we can guarantee that one of each colour has been selected since there must be achance of placing two balls of the same colour in the bag.
   So in neither case is probability a factor.

 

1 hour ago, b_alsept@alsept said:

To explain something at the atomic level would take a lot more time and space than we have here, but it can be done. Because you asked, I'll show how adding a time dependent property to a particle, totally changes the probability of it passing a slit. You'll see it matches QM predictions.

Malus Law or cos2theta is found just about everywhere in QM, including one simple experiment where particles are sent through multiple polarizers set at different angles. I realize this is not the double slit experiment but it does explain the effect that a time dependent property has on the chances of a particle making it through a slit.

etc

 

Thank you for you input and sharp example.

However I do not see where entanglement could occcur in this example ?

 

Once again thank you all for helping me clarify my thoughts on this difficult subject

[swansont]

13 hours ago, b_alsept@alsept said:

They are intentionally correlated.

Will you explain how?

I really hope you aren’t going to make me keep asking you for specifics. 

6 hours ago, b_alsept@alsept said:

Instead of photons or electrons I'll use larger objects to help demonstrate this. Of course testing one particle/object would not be enough. I’m talking about testing thousands, at multiple set points. I could choose from hundreds of different objects but to be analogous and to make a point, let’s say the objects are 30cm-long throwing knives, 40mm tall and 5mm thick.

There’s no quantum mechanics here, thus, no entanglement 

5 hours ago, Markus Hanke said:

Yes, of course. But what I meant here isn’t the maximum correlation (which is always 1 of course), but how it is distributed as a function of detector angle in the classical Bell experiment (graph taken from Wiki). You can see the quantum correlation is stronger than classical correlation (local realism):

But it has to be a Bell experiment, which is not generally the case.

5 hours ago, studiot said:

Two particles can be 'entangled' if they have a binary property ie that can be measured in one of two states.

It must be the case that you can’t separate the wave function - it’s in a superposition of the states.

[b_alsept@alsept]

1 hour ago, swansont said:

There’s no quantum mechanics here, thus, no entanglement 

All the talk of entanglement and spooky action at a distance creates confusion and distracts us from the real question. Why does the interference pattern form?

One camp claims that particles are either going through both slits at the same time or two particles are (not correlated) but somehow magically entangled.

The other camp claims the particles go through one slit only before being detected at the screen and their properties were already set from the start. Einstein was in this camp and his original thought experiment had nothing to do with entanglement but everything to do with correlation. He imagined two particles perfectly correlated or anti-correlated so that the speed, polarization, direction and linear dependency were exactly the same. Then you could later measure one particle and know everything about the other without disturbing it. Like I said the multi-polarizer experiment was not the same as the correlating two particles experiment but they both share the idea that a particle can (and does) have more properties than just polarization.

[studiot]

12 minutes ago, b_alsept@alsept said:

All the talk of entanglement and spooky action at a distance creates confusion and distracts us from the real question. Why does the interference pattern form?

Are you sure you posted this in the right thread ?

We have two current threads discussing the nature of interference and 'the slits experiments'.

This one couldn't be more clearly about entanglement.

 

Your input to entanglement is, however welcome.

2 hours ago, swansont said:

It must be the case that you can’t separate the wave function - it’s in a superposition of the states.

I see that your opinion is that entanglement is only applicable to 'quantum systems' ie to quantum description of systems, whatever they may be.

I see opinion is divided on this.

And of course the object of this thread is to give the whole subject a proper airing.

So fire away.

 

https://www.google.co.uk/search?q=classical+entanglement&source=hp&ei=79B-YYihJq2dlwS4hI-gBg&iflsig=ALs-wAMAAAAAYX7e_3e-xUlFE4jFLwPsk6BgDmf6Prqt&oq=classical+entanglement&gs_lcp=Cgdnd3Mtd2l6EAMyBQgAEIAEMgYIABAWEB4yBggAEBYQHjIGCAAQFhAeMgYIABAWEB4yBggAEBYQHjIGCAAQFhAeMgYIABAWEB4yBggAEBYQHjIGCAAQFhAeOhEILhCABBCxAxDHARCjAhCTAjoICAAQgAQQsQM6DgguEIAEELEDEMcBEKMCOg4ILhCABBCxAxDHARDRAzoLCAAQgAQQsQMQgwE6CAgAELEDEIMBOggILhCABBCxAzoLCC4QgAQQxwEQrwE6DgguEIAEELEDEMcBEK8BOhEILhCABBCxAxCDARDHARCjAjoFCC4QgAQ6CwgAEIAEELEDEMkDOgUIABCSAzoRCC4QgAQQsQMQxwEQ0QMQkwI6CwguEIAEEMcBENEDOgUIABCxAzoHCAAQgAQQClDKCVjgJmCGKWgAcAB4AoABxAWIAeJGkgEOMC4xLjAuNi4xMC4zLjGYAQCgAQE&sclient=gws-wiz&ved=0ahUKEwjI1PH8lPXzAhWtzoUKHTjCA2QQ4dUDCAk&uact=5

Edited October 31, 2021 by studiot

[b_alsept@alsept]

17 hours ago, Markus Hanke said:

Yes, of course. But what I meant here isn’t the maximum correlation (which is always 1 of course), but how it is distributed as a function of detector angle in the classical Bell experiment (graph taken from Wiki). You can see the quantum correlation is stronger than classical correlation (local realism):

Two post before you posted the classical Bell Graph, I described how a multiple polarizer (another quantum mechanical experiment) could explain (local realism) with real objects. The results of this experiment (which are not linear) are usually described as QM because no one can explain the (cos2theta) results classically. I show that particles can have  (real properties) that explain the experimental results, agreeing with QM predictions and follow Malus Law/cos2theta which is shown in blue, on your graph. 

[Markus Hanke]

39 minutes ago, b_alsept@alsept said:

Two post before you posted the classical Bell Graph, I described how a multiple polarizer (another quantum mechanical experiment) could explain (local realism) with real objects. The results of this experiment (which are not linear) are usually described as QM because no one can explain the (cos2theta) results classically. I show that particles can have  (real properties) that explain the experimental results, agreeing with QM predictions and follow Malus Law/cos2theta which is shown in blue, on your graph. 

This appears to be better suited for a new, dedicated thread; it doesn’t quite fit into this discussion.

[b_alsept@alsept]

2 hours ago, Markus Hanke said:

This appears to be better suited for a new, dedicated thread; it doesn’t quite fit into this discussion.

Thanks, you are right.

[swansont]

17 hours ago, studiot said:

Are you sure you posted this in the right thread ?

We have two current threads discussing the nature of interference and 'the slits experiments'.

This one couldn't be more clearly about entanglement.

 

Your input to entanglement is, however welcome.

I see that your opinion is that entanglement is only applicable to 'quantum systems' ie to quantum description of systems, whatever they may be.

I see opinion is divided on this.

And of course the object of this thread is to give the whole subject a proper airing.

So fire away.

 

https://www.google.co.uk/search?q=classical+entanglement&source=hp&ei=79B-YYihJq2dlwS4hI-gBg&iflsig=ALs-wAMAAAAAYX7e_3e-xUlFE4jFLwPsk6BgDmf6Prqt&oq=classical+entanglement&gs_lcp=Cgdnd3Mtd2l6EAMyBQgAEIAEMgYIABAWEB4yBggAEBYQHjIGCAAQFhAeMgYIABAWEB4yBggAEBYQHjIGCAAQFhAeMgYIABAWEB4yBggAEBYQHjIGCAAQFhAeOhEILhCABBCxAxDHARCjAhCTAjoICAAQgAQQsQM6DgguEIAEELEDEMcBEKMCOg4ILhCABBCxAxDHARDRAzoLCAAQgAQQsQMQgwE6CAgAELEDEIMBOggILhCABBCxAzoLCC4QgAQQxwEQrwE6DgguEIAEELEDEMcBEK8BOhEILhCABBCxAxCDARDHARCjAjoFCC4QgAQ6CwgAEIAEELEDEMkDOgUIABCSAzoRCC4QgAQQsQMQxwEQ0QMQkwI6CwguEIAEEMcBENEDOgUIABCxAzoHCAAQgAQQClDKCVjgJmCGKWgAcAB4AoABxAWIAeJGkgEOMC4xLjAuNi4xMC4zLjGYAQCgAQE&sclient=gws-wiz&ved=0ahUKEwjI1PH8lPXzAhWtzoUKHTjCA2QQ4dUDCAk&uact=5

The term "entanglement" entered the scientific lexicon after the EPR paradox paper was published, in a response by Schrödinger. He used a German term (Verschränkung), and translated that as entanglement.

"I would not call [entanglement] one but rather the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought."

https://en.wikipedia.org/wiki/Quantum_entanglement

So the person that coined the term did so to describe quantum behavior and argued that entanglement was a purely quantum phenomenon. It's used to describe a situation that cannot be replicated in classical systems, which means there is no classical entanglement.  

[studiot]

 

1 hour ago, swansont said:

The term "entanglement" entered the scientific lexicon after the EPR paradox paper was published, in a response by Schrödinger. He used a German term (Verschränkung), and translated that as entanglement.

"I would not call [entanglement] one but rather the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought."

https://en.wikipedia.org/wiki/Quantum_entanglement

So the person that coined the term did so to describe quantum behavior and argued that entanglement was a purely quantum phenomenon. It's used to describe a situation that cannot be replicated in classical systems, which means there is no classical entanglement.  

Thank you for this interesting point of history, although I don't see what the has to do with the slit experiments I referred to.

 

Schrodinger was a professor of (Applied) Mathematics.
Mathematicains are ,of course, the world's greatest generalisers.
As such I am sure that S would be happy to see his description generalised, rather as the original definitions of vectors and many other quantities have been generalised.

 

Quoting from your link (which seems to me to be generally pretty well written) I am puzzled by this

Quote

In entanglement, one constituent cannot be fully described without considering the other(s).

Why is it necessary to consider the spin of both entangled electrons in an orbital ?

If you know one you know the other, but you don't have to know the other in order to know the one.

[swansont]

1 hour ago, studiot said:

 

Thank you for this interesting point of history, although I don't see what the has to do with the slit experiments I referred to.

 

You said

I see opinion is divided on this.

And of course the object of this thread is to give the whole subject a proper airing.

which is the bit I was responding to

 

1 hour ago, studiot said:

Schrodinger was a professor of (Applied) Mathematics.
Mathematicains are ,of course, the world's greatest generalisers.

As such I am sure that S would be happy to see his description generalised, rather as the original definitions of vectors and many other quantities have been generalised.

Seeing as he described something as THE characteristic trait of QM, it doesn't sound to me like generalization would be embraced in this case. Plus the faulty syllogism (that mathematicians generalize some things, does not imply all mathematicians generalize all things)

 

 

1 hour ago, studiot said:

Quoting from your link (which seems to me to be generally pretty well written) I am puzzled by this

Why is it necessary to consider the spin of both entangled electrons in an orbital ?

If you know one you know the other, but you don't have to know the other in order to know the one.

The description is of the system before measurement, before you know the state of a particular electron.