QM Assumptions Regarding Entanglement Properties

[Dadface]

In a nutshell I think that in local realistic theories it is assumed that:

Each entangled object has definite properties at all times, even when not observed.

I know the assumption is proved to be incorrect but is that an assumption actually made in such theories?But what assumptions about properties, if any, are made in QM? Are either of the following assumptions made?

When not observed each object has the property of existing in all possible states simultaneously but observations reveal one state only for each object.

Each object cannot be described as having properties at all, until and unless an observation is made.

Are there other assumptions and do the assumptions made depend on what interpretation of QM is used?

Thanks to anyone who replies

 

[Zafa Pi]

In a nutshell I think that in local realistic theories it is assumed that:

Each entangled object has definite properties at all times, even when not observed.
This depends on which properties. If the objects are electrons then they maintain that property. However, often one cannot ascribe a particular state to entangled objects.
I know the assumption is proved to be incorrect but is that an assumption actually made in such theories?
In proving Bell type theorems the assumption of realism or counter factual definiteness is often made.
But what assumptions about properties, if any, are made in QM? Are either of the following assumptions made?

When not observed each object has the property of existing in all possible states simultaneously but observations reveal one state only for each object.
If not entangled an object has a particular state that evolves over time. Observations may "collapse" (old school) that state to one of several possible (eigen)states.
Each object cannot be described as having properties at all, until and unless an observation is made.
No. It may be prepared in a known state.
Are there other assumptions and do the assumptions made depend on what interpretation of QM is used?
Yes, e.g. how the states change with time is the same for most all interpretations. And some assumptions depend on interpretations.
Thanks to anyone who replies

I think it would be of help if you chose to do some reading in a beginners text.

 

[Dadface]

Thank you Zafa Pi. Your advice is good but I have done so much reading on this subject that my teeth are beginning to itch. I have gone through some texts several times. I think I have the general idea about entanglement, Bell and Bell tests but I'm stuck on what I think are very relevant assumptions made by local realists and by QM adherents. There is something that seems a bit strange and perhaps contradictory to me and I can't even quite pin down what it is. It's just a feeling. Hence my post above which was asking for clarification. Please allow me to comment on each of your five comments above.

1. The properties I referred to are the entangled properties whatever they may be, for example entangled spins or polarisations.

2. As I understand it realists believe(d) that the non entangled and entangled properties of each entangled particle has definite values at all times.

3. 4. 5. I'm fine with those comments.However, I had forgotten that objects can be prepared in a known state.

Mainly what I want to know is whether or not, what I have written in note two above is correct. The assumption of "definite properties at all times" covers realism and counter factual definiteness. I think.

Now if what I have written in note two is correct can I further assume that Bell test experiments disprove the assumptions made by realists as in note two? Is it that simple? If so I'm finding it rather odd.

 

[Zafa Pi]

Thank you Zafa Pi. Your advice is good but I have done so much reading on this subject that my teeth are beginning to itch. I have gone through some texts several times. I think I have the general idea about entanglement, Bell and Bell tests but I'm stuck on what I think are very relevant assumptions made by local realists and by QM adherents. There is something that seems a bit strange and perhaps contradictory to me and I can't even quite pin down what it is. It's just a feeling. Hence my post above which was asking for clarification. Please allow me to comment on each of your five comments above.

1. The properties I referred to are the entangled properties whatever they may be, for example entangled spins or polarisations.

2. As I understand it realists believe(d) that the non entangled and entangled properties of each entangled particle has definite values at all times.

3. 4. 5. I'm fine with those comments.However, I had forgotten that objects can be prepared in a known state.

Mainly what I want to know is whether or not, what I have written in note two above is correct. The assumption of "definite properties at all times" covers realism and counter factual definiteness. I think.

Now if what I have written in note two is correct can I further assume that Bell test experiments disprove the assumptions made by realists as in note two? Is it that simple? If so I'm finding it rather odd.

I suggest that you pick a particular short article (e.g. wiki) on Bell's theorem, or entanglement and we can go from there.

 

[Dadface]

thank you again Zafa Pi. I will take your advice and look at some of the literature again and probably find some new stuff to look at. I shall probably have time at the weekend to do that properly.
I should point out that I am reasonably familiar with entanglement, Bell theory and Bell tests, the concept of local realism etc but I'm just stuck on one thing that goes right back to first principles That one thing is the assumptions made by local realistic theories.

Do all local realistic theories assume that, along with the principle of locality, each entangled object has real properties even before observations are made.

In a nutshell that's all I want to know. Everything I've read so far seems to claim the above assumption is made but the assumption seems strange and that's what's niggling me. Hence it would be nice to get the views from an expert to confirm,or otherwise that the assumption is made (and proved to be incorrect by Bell test experiments).

 

[Zafa Pi]

thank you again Zafa Pi. I will take your advice and look at some of the literature again and probably find some new stuff to look at. I shall probably have time at the weekend to do that properly.
I should point out that I am reasonably familiar with entanglement, Bell theory and Bell tests, the concept of local realism etc but I'm just stuck on one thing that goes right back to first principles That one thing is the assumptions made by local realistic theories.

Do all local realistic theories assume that, along with the principle of locality, each entangled object has real properties even before observations are made.

In a nutshell that's all I want to know. Everything I've read so far seems to claim the above assumption is made but the assumption seems strange and that's what's niggling me. Hence it would be nice to get the views from an expert to confirm,or otherwise that the assumption is made (and proved to be incorrect by Bell test experiments).

I'm not an expert
You should specify which properties you are referring to. The QM view of an entangled particle is that it has no state.
In proving Bell's Theorem, besides locality, one of the following is assumed (with my take):
Realism: Alice's measurement result does not depend on which measurement that Bob makes.
Hidden variables: The particles measured come endowed with proscribed values for each measurement. (Is this your "has real properties even before observations are made"?)
Counter factual definiteness: A particle will have some value (unknown) if measured, regardless of whether it's measured.

I prefer using CFD in proofs of Bell's theorems because it seems the most intuitive, and arises naturally.

You might like this elementary way to distinguish classical from quantum.
Let us suppose that:
1) Alice and Bob are isolated from one another, so that no communication or influence can pass between them and neither knows what the other is doing.
2) If Alice and Bob both perform experiment X they will get the same result.
3) Alice performs experiment X and gets value 0, while Bob performs experiment Y and gets 1.
Then
4) If Bob had performed X instead of Y would he have necessarily gotten 0?

Classical physics says yes and quantum physics says no.

With classical physics we know that the reality facing Alice is unaffected by what Bob does, so she would have had to get 0 if Bob did X instead, and thus yes, Bob must get 0 because of 2).

The classical argument above is sufficient to derive Bell's inequality which is denied by quantum physics thus yielding no.

The question posed by 1), 2), 3), and 4) is both short and requires no knowledge of physics.

 

[zonde]

In a nutshell that's all I want to know. Everything I've read so far seems to claim the above assumption is made but the assumption seems strange and that's what's niggling me. Hence it would be nice to get the views from an expert to confirm,or otherwise that the assumption is made (and proved to be incorrect by Bell test experiments).

Small correction. Bell test experiments do not falsify that particles have properties before measured. Instead what they falsify is that "particles having properties before measured" alone can not explain entanglement. So to explain entanglement you might speculate that particles have properties plus some additional physical mechanism. Or you might speculate that particles don't have properties, but then you would have to give some alternative explanation for phenomena like linearly polarized light.

 

[Zafa Pi]

Small correction. Bell test experiments do not falsify that particles have properties before measured. Instead what they falsify is that "particles having properties before measured" alone can not explain entanglement. So to explain entanglement you might speculate that particles have properties plus some additional physical mechanism. Or you might speculate that particles don't have properties, but then you would have to give some alternative explanation for phenomena like linearly polarized light.

I'm confused. At the beginning of the paragraph you are talking about entangled particles. But in the last sentence are you still talking about entangled particles?

 

[Dadface]

Mainly what I'm trying to find is a simple yet rigorous description (one that can be understood by an interested amateur) of what exactly it is that Bells theory disproves. I have looked at many papers on this including the original EPR paper but I think the quote below is close to what I'm looking for:

Below is the quote which is from a Wiki article on "Principle of Locality"

"Einsteins principle of local realism is the combination of the principle of locality (limiting cause-and-effect to the speed of light) with the assumption that a particle must objectively have pre-existing value (ie a real value) for any possible measurement ie a value existing before that measurement is made".

I think the description is simple but can it be considered to be rigorous? I have a few points that I would like to be clarified if possible

1. Does the word value refer to anything and everything that can be measured, including, with the electron as an example, properties (such as electron mass) and non properties ( such as electron location at a particular instant)?
2. Can the reference to locality be ignored since if particles have pre-existing values the reference to light speed seems irrelevant?
Thank you

 

[Dadface]

Small correction. Bell test experiments do not falsify that particles have properties before measured. Instead what they falsify is that "particles having properties before measured" alone can not explain entanglement. So to explain entanglement you might speculate that particles have properties plus some additional physical mechanism. Or you might speculate that particles don't have properties, but then you would have to give some alternative explanation for phenomena like linearly polarized light.

Thank you zonde is the "additional physical mechanism" you refer to equivalent to the "hidden variables concept " referred to in EPR? If so, if Bell tests falsify the idea that particles have real properties etc do not the tests also falsify the concept of hidden variables?

 

[zonde]

I have looked at many papers on this including the original EPR paper but I think the quote below is close to what I'm looking for:

Below is the quote which is from a Wiki article on "Principle of Locality"

"Einsteins principle of local realism is the combination of the principle of locality (limiting cause-and-effect to the speed of light) with the assumption that a particle must objectively have pre-existing value (ie a real value) for any possible measurement ie a value existing before that measurement is made".

I think the description is simple but can it be considered to be rigorous?

No, it can't. You say you have read original EPR paper, can't you spot discrepancy? In EPR paper realism is mentioned right at the end of first page.

 

[zonde]

Thank you zonde is the "additional physical mechanism" you refer to equivalent to the "hidden variables concept " referred to in EPR?

No.

If so, if Bell tests falsify the idea that particles have real properties etc do not the tests also falsify the concept of hidden variables?

Experiment can not falsify a concept. Experiment can falsify a model.

 

[Dadface]

Mainly what I'm trying to find is a simple yet rigorous description (one that can be understood by an interested amateur) of what exactly it is that Bells theory disproves. I have looked at many papers on this including the original EPR paper but I think the quote below is close to what I'm looking for:

Below is the quote which is from a Wiki article on "Principle of Locality"

"Einsteins principle of local realism is the combination of the principle of locality (limiting cause-and-effect to the speed of light) with the assumption that a particle must objectively have pre-existing value (ie a real value) for any possible measurement ie a value existing before that measurement is made".

I think the description is simple but can it be considered to be rigorous? I have a few points that I would like to be clarified if possible

1. Does the word value refer to anything and everything that can be measured, including, with the electron as an example, properties (such as electron mass) and non properties ( such as electron location at a particular instant)?
2. Can the reference to locality be ignored since if particles have pre-existing values the reference to light speed seems irrelevant?
Thank you

No, it can't. You say you have read original EPR paper, can't you spot discrepancy? In EPR paper realism is mentioned right at the end of first page.

You must be referring to the notes in italics and from how I interpret them they are equivalent to the notes i referred to in the Wiki article For example "if we can predict with certainty the value of a physical quantity etc" (EPR paper) seems to imply that "a particle must have pre-existing values etc (Wiki article). So I can't yet spot a discrepancy other than the use of different words to describe the same thing. However I'm in a rush at present so I will go back and take a closer look at it. Thanks for your input.

 

[Dadface]

No.
Experiment can not falsify a concept. Experiment can falsify a model.

You answered no to the first question so what is the additional physical mechanism you referred to?

Models are built on concepts.

Sorry I'm writing this in a rush but will get back to it. But thank you very much.

 

[rede96]

Let us suppose that:
1) Alice and Bob are isolated from one another, so that no communication or influence can pass between them and neither knows what the other is doing.
2) If Alice and Bob both perform experiment X they will get the same result.
3) Alice performs experiment X and gets value 0, while Bob performs experiment Y and gets 1.
Then
4) If Bob had performed X instead of Y would he have necessarily gotten 0?

Classical physics says yes and quantum physics says no.

With classical physics we know that the reality facing Alice is unaffected by what Bob does, so she would have had to get 0 if Bob did X instead, and thus yes, Bob must get 0 because of 2).

The classical argument above is sufficient to derive Bell's inequality which is denied by quantum physics thus yielding no.

The question posed by 1), 2), 3), and 4) is both short and requires no knowledge of physics.

Just out of curiosity, if Alice and Bob *always* get the same results when they perform the same experiment how does QM predict something different?

If it did then Alice and Bob wouldn’t always get the same result when they performed the same experiment.

 

[entropy1]

2. As I understand it realists believe(d) that the non entangled and entangled properties of each entangled particle has definite values at all times.
[..]
Now if what I have written in note two is correct can I further assume that Bell test experiments disprove the assumptions made by realists as in note two? Is it that simple? If so I'm finding it rather odd.

If in note 2 you mean local hidden variables, they are refuted by Bell's ineq. AFAIK.

 

[jerromyjon]

Just out of curiosity, if Alice and Bob *always* get the same results when they perform the same experiment how does QM predict something different?

The difference lies in the fact that correlations at different angles produce different probabilities. The 100% correlation isn't what changes from classical theories, it is the cos(θ) which describes quantum probability in the intermediate angles. (please forgive me and correct me, mentors, if that isn't the most explicit way to describe it)

 

[Zafa Pi]

Just out of curiosity, if Alice and Bob *always* get the same results when they perform the same experiment how does QM predict something different?

If it did then Alice and Bob wouldn’t always get the same result when they performed the same experiment.

I only assumed they would get the same result if they both performed experiment X. It doesn't hold for other experiments.

 

[jerromyjon]

I only assumed they would get the same result if they both performed experiment X. It doesn't hold for other experiments.

I can't begin to imagine what you mean by that "assumption". I have read many papers on various experiments where "Alice & Bob" got confirmation of quantum entanglement in their results...

 

[Zafa Pi]

I can't begin to imagine what you mean by that "assumption". I have read many papers on various experiments where "Alice & Bob" got confirmation of quantum entanglement in their results...

In post #16 I proposed a situation governed by 1), 2), and 3). Then I asked a question in 4). After that I gave an answer to that question. Can you specify more clearly where your problem lies?

 

[OCR]

In post #16 I proposed a situation...

Wasn't the original post a response to Dadface... post #7 ?

However... post #16 works as well...I DO read all of your posts, you know... .

 

[Zafa Pi]

Wasn't the original post a response to Dadface... post #7 ?
You are absolutely correct. But that post has more stuff on it.
However... post #16 works as well...I DO read all of your posts, you know... .

That's flattering, but I think Louis CK and Sarah Silverman are funnier.

 

[jerromyjon]

Can you specify more clearly where your problem lies?

Alice and Bob are generic terms for space separated observers. When they compare results of measurements of quantum particles at random angles (In any given experiment!) they concur that quantum entanglement was involved... by the probabilities of quantum correlations.

 

[zonde]

You must be referring to the notes in italics and from how I interpret them they are equivalent to the notes i referred to in the Wiki article For example "if we can predict with certainty the value of a physical quantity etc" (EPR paper) seems to imply that "a particle must have pre-existing values etc (Wiki article). So I can't yet spot a discrepancy other than the use of different words to describe the same thing. However I'm in a rush at present so I will go back and take a closer look at it. Thanks for your input.

Let me write two sentences:
"there exists an element of physical reality if we can predict with certainty the value of a physical quantity" (EPR paper)
"a particle must objectively have pre-existing value for any possible measurement" (Wiki article)
Would you still claim that these two sentences are saying basically the same thing just using different words?

 

[zonde]

You answered no to the first question so what is the additional physical mechanism you referred to?

FTL effect.

Models are built on concepts.

So what? Do you imply that one can not build invalid model using valid concepts?

 

[Dadface]

Let me write two sentences:
"there exists an element of physical reality if we can predict with certainty the value of a physical quantity" (EPR paper)
"a particle must objectively have pre-existing value for any possible measurement" (Wiki article)
Would you still claim that these two sentences are saying basically the same thing just using different words?

EPR refers to the..... "value of a physical quantity" that can be "predicted with certainty"........ . In other words the (unspecified) physical quantity has a value which would be revealed ......"for any possible measurement" (WIKI)

In other words if we can "predict with certainty the value" That value would be known (pre-exist) when and if we confirm the prediction by making suitable observations (any possible measurements)

 

[Dadface]

FTL effect.

Please look again at post 6 post and post 8. I think the principle of locality referred to in 6 covers what you describe as "FTL effect"

So what? Do you imply that one can not build invalid model using valid concepts?

I don't think this is relevant. I wasn't referring to concepts in general I was referring to one specific concept... hidden variables.

 

[Dadface]

This thread seems to be going in different directions which is fine by me. I would however appreciate it if anyone could come up with the following.

A rigorous yet simple (one that can be understood by an interested amateur) description of what exactly it is that Bell's theory disproves.

See post 10

Thank you

 

[MarekKuzmicki]

But what assumptions about properties, if any, are made in QM?

There is 'uncertainty principle'.

 

[Zafa Pi]

Alice and Bob are generic terms for space separated observers. When they compare results of measurements of quantum particles at random angles (In any given experiment!) they concur that quantum entanglement was involved... by the probabilities of quantum correlations.

If you allow for a number of runs at the various angles in order to gather sufficient statistics, then, yes you are correct. But what has that got to do with my construction in post #16? If you have a problem with it just tell me where it is.

 

[Zafa Pi]

I would however appreciate it if anyone could come up with the following.
A rigorous yet simple (one that can be understood by an interested amateur) description of what exactly it is that Bell's theory disproves.

Bell allegedly does this in the 1st page of his original 1964 paper. However, I find Bell quite muddled and the reason all this argument goes on. This is not a very popular point of view.

His use of the phrase "if the two measurements are made at places remote from one another" indicates to me that locality means no FTL communication.

I think that the 1st sentence that @zonde gives in post #25 implies (along with EPR asking for hidden variables) the 2nd in the case of an entangled pair.

I sum this up in your favor: No theory assuming Locality (no FLT) and hidden variables (entangled pairs have predetermined values just prior to measurement) can reproduce the measurements made in reality (or predicted by QM).

Now wait for experts to say I'm wrong.

 

[Lord Jestocost]

This thread seems to be going in different directions which is fine by me. I would however appreciate it if anyone could come up with the following.

A rigorous yet simple (one that can be understood by an interested amateur) description of what exactly it is that Bell's theory disproves.

Bell shows that the classical concept of separability or locality is incompatible with the statistical predictions of quantum mechanics when considering entangled^* quantum mechanical entities (I personally prefer the term separability). That's the point, and his paper doesn’t touch – to my mind – on questions regarding realism. Here is the abstract from the paper “On the Einstein-Podolsky-Rosen paradox” by J. S. Bell (in: Physics, vol. 1, number 3, 1964, pp. 195–200):

“THE paradox of Einstein, Podolsky and Rosen [1] was advanced as an argument that quantum mechanics could not be a complete theory but should be supplemented by additional variables. These additional variables were to restore to the theory causality and locality [2]. In this note that idea will be formulated mathematically and shown to be incompatible with the statistical predictions of quantum mechanics. It is the requirement of locality, or more precisely that the result of a measurement on one system be unaffected by operations on a distant system with which it has interacted in the past, that creates the essential difficulty. There have been attempts [3] to show that even without such a separability or locality requirement no "hidden variable" interpretation of quantum mechanics is possible. These attempts have been examined elsewhere [4] and found wanting. Moreover, a hidden variable interpretation of elementary quantum theory [5] has been explicitly constructed. That particular interpretation has indeed a grossly nonlocal structure. This is characteristic, according to the result to be proved here, of any such theory which reproduces exactly the quantum mechanical predictions.”

^*Regarding entanglement, here is quote from E. Schroedinger ("Discussion of probability relations between separate systems", Proceedings of the Cambridge Philosophical Society, 31, 1935)

“When two systems, of which we know the states by their respective representatives, enter into temporary physical interaction due to known forces between them, and when after a time of mutual influence the systems separate again, then they can no longer be described in the same way as before, viz. by endowing each of them with a representative of its own. I would not call that one but rather the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought. By the interaction the two representatives (or ψ-functions) have become entangled.”

 

[Dadface]

Bell allegedly does this in the 1st page of his original 1964 paper. However, I find Bell quite muddled and the reason all this argument goes on. This is not a very popular point of view.

His use of the phrase "if the two measurements are made at places remote from one another" indicates to me that locality means no FTL communication.

I think that the 1st sentence that @zonde gives in post #25 implies (along with EPR asking for hidden variables) the 2nd in the case of an entangled pair.

I sum this up in your favor: No theory assuming Locality (no FLT) and hidden variables (entangled pairs have predetermined values just prior to measurement) can reproduce the measurements made in reality (or predicted by QM).

Now wait for experts to say I'm wrong.

Thank you very much Zafa Pi. I think your summing up is both rigorous and understandable and as an added bonus concise as well. It will be interesting to see if other experts have comments to add.
(I know you said you weren't an expert but you certainly seem to be very knowledgeable on the subject)

 

[Dadface]

Bell shows that the classical concept of separability or locality is incompatible with the statistical predictions of quantum mechanics when considering entangled^* quantum mechanical entities (I personally prefer the term separability). That's the point, and his paper doesn’t touch – to my mind – on questions regarding realism. Here is the abstract from the paper “On the Einstein-Podolsky-Rosen paradox” by J. S. Bell (in: Physics, vol. 1, number 3, 1964, pp. 195–200):

“THE paradox of Einstein, Podolsky and Rosen [1] was advanced as an argument that quantum mechanics could not be a complete theory but should be supplemented by additional variables. These additional variables were to restore to the theory causality and locality [2]. In this note that idea will be formulated mathematically and shown to be incompatible with the statistical predictions of quantum mechanics. It is the requirement of locality, or more precisely that the result of a measurement on one system be unaffected by operations on a distant system with which it has interacted in the past, that creates the essential difficulty. There have been attempts [3] to show that even without such a separability or locality requirement no "hidden variable" interpretation of quantum mechanics is possible. These attempts have been examined elsewhere [4] and found wanting. Moreover, a hidden variable interpretation of elementary quantum theory [5] has been explicitly constructed. That particular interpretation has indeed a grossly nonlocal structure. This is characteristic, according to the result to be proved here, of any such theory which reproduces exactly the quantum mechanical predictions.”

^*Regarding entanglement, here is quote from E. Schroedinger ("Discussion of probability relations between separate systems", Proceedings of the Cambridge Philosophical Society, 31, 1935)

“When two systems, of which we know the states by their respective representatives, enter into temporary physical interaction due to known forces between them, and when after a time of mutual influence the systems separate again, then they can no longer be described in the same way as before, viz. by endowing each of them with a representative of its own. I would not call that one but rather the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought. By the interaction the two representatives (or ψ-functions) have become entangled.”

Thanks Lord Jescott. The EPR paper and Bells paper are both rather old now and I think it's safe to say that both works have been clarified and/or developed further. Is it safe to say that? The point I would like to make is that it seems to me, from my readings and advice given here on PF, that newer accounts of Bell's work do touch on questions of realism. Is that the case?

 

[Lord Jestocost]

The EPR paper and Bells paper are both rather old now and I think it's safe to say that both works have been clarified and/or developed further. Is it safe to say that?

To my mind, these papers need no further clarification.