I 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.

 

[zonde]

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)

I would like to ask you: according to EPR should we assume that physical quantity has preexisting value when we can't predict it with certainty (but we can measure it)?

 

[Jilang]

It seems clear that hidden variables cannot be coded in the probability, however they can be in the probability amplitudes, see here as SD demonstrates at post #66.
https://www.physicsforums.com/threa...-bell-correlations.930853/page-4#post-5885421
The issue we all have, as I see it, is that probality amplitudes don’t need to be be “real” and can be complex. I would suggest that this should be interpreted a quantum reality (as opposed to a classical one) that the maths describes beautifully, but that we don’t quite understand it yet. (There is no need to dispense with locality or reality right now).

 

[Mentz114]

I would like to ask you: according to EPR should we assume that physical quantity has preexisting value when we can't predict it with certainty (but we can measure it)?

If I could add a comment on this tricky subject. Surely it depends on which physical quantity you consider ?
The Hamiltonian ($H$)requires that there be values for its components at all times. So if there is a potental term and and a kinetic term in $H$ then $p$ and $x$ must have values even when not measured. The confusion comes if $H$ has an angular momentum term. $H$ does not tell us about the orientation of the angular momentum which is something we can measure. In order to measure it we construct ( or assume) a coordinate system and use apparatus whose alignment determines the direction of the measurement. The measurement is projective and some objects whose spin alignment is not exactly along and axis will be re-aligned so they are. This is all well known and understood and it is the origin of the assertion that we cannot sensibly say that an object has spin alignment in this or that direction until the measurement is carried out. There's nothing strange here. Until we go through the mental and physical processes of setting up and measuring it is meaningless to ascribe a value to spin orientation.

 

[Jilang]

If I could add a comment on this tricky subject. Surely it depends on which physical quantity you consider ? This is all well known and understood and it is the origin of the assertion that we cannot sensibly say that an object has spin alignment in this or that direction until the measurement is carried out. There's nothing strange here. Until we go through the mental and physical processes of setting up and measuring it is meaningless to ascribe a value to spin orientation.

Just so. But are we able to describe a hidden variable that will predict the probability of what will happen when such a measurement is made? It seems that on some level we can, but the description is not “real” in the way classical physics would describe it.

 

[Mentz114]

Just so.
But are we able to describe a hidden variable that will predict the probability of what will happen when such a measurement is made?

The Bell experiment is conducted on prepared (pre-projected) states and we can say that this state is a superposition $a|\uparrow\downarrow\rangle + a|\downarrow\uparrow\rangle,\ \ 2 |a|^2=1$. My own view is that the value of the preparation is already chosen and is actually fixed ( pre-projected) to $|\uparrow\downarrow\rangle$ or $|\downarrow\uparrow\rangle$. It is the 'hidden' variable. It is said that this violates EPR/Bell but I don't see how.

 

[Jilang]

The Bell experiment is conducted on prepared (pre-projected) states and we can say that this state is a superposition $a|\uparrow\downarrow\rangle + a|\downarrow\uparrow\rangle,\ \ 2 |a|^2=1$. My own view is that the value of the preparation is already chosen and is actually fixed ( pre-projected) to $|\uparrow\downarrow\rangle$ or $|\downarrow\uparrow\rangle$. It is the 'hidden' variable. It is said that this violates EPR/Bell but I don't see how.

Like I said. It is encoded in the amplitude rather than the probability and only probabilities are real.

 

[Mentz114]

Like I said. It is encoded in the amplitude rather than the probability and only probabilities are real.

Referring to @stevendaryl s post, he concludes

I don't know physically what it means that amplitudes, rather than probabilities factor, but it shows that quantum problems are often a lot simpler in terms of amplitudes.

It seems to support my own inclinations ( as if that matters ).
But whether this means we can have a hidden variable - I can't answer that now or maybe ever. I mean non-local HVs have not been ruled out have they ?

 

[Dadface]

To my mind, these papers need no further clarification.

But I think they were clarified. According to the Stanford Encyclopaedia of Philosophy the original Bell paper was "relaxed" in later years. By Bell himself in 71, 85 and 87 and also by others including Clauser, Horne , Mermin Aspect and others. I don't know if these later works give greater insights.

 

[Dadface]

I would like to ask you: according to EPR should we assume that physical quantity has preexisting value when we can't predict it with certainty (but we can measure it)?

This is the sort of question I have been trying to get other peoples opinions on. See the opening question in post one. I have my own opinion about the answer but am not yet convinced that what i think is correct. As you probably know personal opinions can change for various reasons for example reading more about the subject. And I am in the process of doing just that, the trouble is finding the time to do it.

 

[zonde]

This is the sort of question I have been trying to get other peoples opinions on. See the opening question in post one. I have my own opinion about the answer but am not yet convinced that what i think is correct.

My answer is that EPR argument does not say (assume) anything about measurements that can not be predicted with certainty. Basically it is irrelevant to EPR argument.

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?

We can only speak about hypothetical local realistic theories of QM phenomena. Apart from that in What Bell Did Maudlin criticizes viewpoint that Bell inequality violations falsify only local hidden variable theories. His argument is that EPR argument show inconsistency between QM and local indeterministic models and Bell extends the argument to local deterministic models. So that EPR+Bell covers all local models that could reproduce QM predictions and show them inconsistent with QM.

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?

I would say that minimal QM gives only statistical prediction about measurements and does not assume anything about individual objects. So assumptions about individual objects should be viewed in context of QM interpretations.

 

[Dadface]

My answer is that EPR argument does not say (assume) anything about measurements that can not be predicted with certainty. Basically it is irrelevant to EPR argument.We can only speak about hypothetical local realistic theories of QM phenomena. Apart from that in What Bell Did Maudlin criticizes viewpoint that Bell inequality violations falsify only local hidden variable theories. His argument is that EPR argument show inconsistency between QM and local indeterministic models and Bell extends the argument to local deterministic models. So that EPR+Bell covers all local models that could reproduce QM predictions and show them inconsistent with QM.I would say that minimal QM gives only statistical prediction about measurements and does not assume anything about individual objects. So assumptions about individual objects should be viewed in context of QM interpretations.

Thank you. I will try to read the Maudlin paper despite the fact that two things put me off.
1. 28 pages!
2. Arxiv. Has Maudlin been accepted by a mainstream journal?

 

[zonde]

2. Arxiv. Has Maudlin been accepted by a mainstream journal?

In arxiv abstract page there is a field "Journal reference". So you can check which arxiv papers are published and where.
For this paper it is: "Journal reference: J. Phys. A: Math. Theor.47 424010, 2014"

 

[Simon Phoenix]

But what assumptions about properties, if any, are made in QM? Are either of the following assumptions made?

Sorry for coming to this a bit late. Been a tad busy

My advice for anyone trying to understand Bell's inequality is to completely forget about QM. The inequality itself is absolutely nothing to do with QM - it is a restriction on plain old probabilities.

What is the BI about then? Well we imagine 2 locations - say Alice's Lab, and Bob's Lab. There's some measuring device at each location. Each device has a dial that can be set to various values - and the devices also have a readout to give the result obtained during the measurement.

So nothing quantum, no assumption about anything at all - just settings and measurement results - just data.

We imagine that Alice and Bob do a whole series of runs of this experiment and then look at the data. So they're going to be able to work out (from the data) things like the probability of getting some result. They're also going to be able to work out (from the data) the probability of getting some result $given$ a particular setting that they chose. And if they get together at some later stage they can also pool their data to work out the joint probabilities.

Let's imagine they've got together to look at their joint data. They find that there's some evidence that their data are correlated. They want to explain this - correlation cries out for explanation. Surely there's some connection between the things they've measured if they're seeing a correlation?

So they make the assumption that there are some set of properties (unmeasured in their experiments) that is the underlying cause for the observed correlation in the data.

So experimentally they can work out the probabilities of particular results $given$ particular device settings, $P(A,B | a,b)$, where $A,B$ are the measurement results they get, respectively and $a,b$ are the respective measurement device settings they chose.

Their assumption of some underlying cause means that really, if they could somehow know the underlying properties, they would have $P(A,B | a,b, \lambda, \mu, . . .)$ where $\lambda, \mu, . . .$ are the values of these underlying properties. It turns out that we can lump all of these underlying properties together and just use the single symbol $\lambda$ to represent all of them. So $\lambda$ just means some set of properties.

These properties 'explain' the observed correlation. What does this mean? Well it means that if we've taken account (or we know) $all$ of these properties then any left over fluctuation in the data has to be independent (if it weren't, if there was still some correlation left, then we wouldn't have captured all of the underlying properties). That means we can write $$P(A,B | a,b, \lambda ) = P(A | a,b, \lambda ) P(B | a,b, \lambda )$$Now of course it would be rather strange to assume that the results in Alice's Lab depend in some way on the $settings$ in Bob's Lab (and vice versa). If there was some dependence we'd have to explain that - there'd have to be some connection, some difference to Alice's set-up when Bob turned his dial to another setting - colloquially we might say that Alice's experimental set-up would 'know' about any changes made to Bob's configuration. So it's very natural to assume that no such connection exists. This is the 'locality' assumption - and it's very reasonable, as you can see!

The upshot is that the conditional joint probability can now (with this locality assumption) be written as $$P(A,B | a,b, \lambda ) = P(A | a, \lambda ) P(B | b, \lambda )$$The last piece is the 'realism' bit - this gets used later on in the derivation where an assumption is made in the math. This assumption is tantamount to saying that properties exist independently of measurement. This is given the fancy name of 'counterfactual definiteness' - but it's really nothing more than a cornerstone of classical physics - in a nutshell it's saying that if I have an object I can measure its position, but I could have measured it's momentum instead an I'd have gotten such and such a value. If you think about it - it's pretty much an underlying assumption of all classical physics. The term 'counterfactual definiteness' just makes it sound like something mysterious and intellectual.

With these entirely reasonable assumptions it can then be shown that there exist constraints on the probability functions - not all choices of function will be consistent (this kind of result, in a totally different context, was derived by Boole a century before Bell - so it's known in classical probability theory). It simply says that given joint distributions of random variables the marginal distributions are constrained. The constraint for our experimental set-up above is, of course, simply the Bell inequality.

No QM here so far - no assumptions of any mechanisms, no 'fields', no 'particles', just measurement results and the probabilities that can be worked out from them and some very natural assumptions about what might be causing any correlation between the data.

The thing is, as we know, there are physical systems we can examine - and when we do the experiments we find the probabilities we work out from the data are not constrained as we expect from the analysis. Therefore at least one of the assumptions we've made in the analysis can't be correct. They might all be incorrect, but at least one has to be decidedly iffy.

So as far as QM is concerned (which does predict the right experimental result) we're saying that QM cannot be wholly replaced by any theory which makes all of these natural assumptions. That's Bell's theorem.

Don't know whether this answers your question or not - but hope it helps frame things a bit.

 

[zonde]

The last piece is the 'realism' bit - this gets used later on in the derivation where an assumption is made in the math. This assumption is tantamount to saying that properties exist independently of measurement. This is given the fancy name of 'counterfactual definiteness' - but it's really nothing more than a cornerstone of classical physics - in a nutshell it's saying that if I have an object I can measure its position, but I could have measured it's momentum instead an I'd have gotten such and such a value. If you think about it - it's pretty much an underlying assumption of all classical physics. The term 'counterfactual definiteness' just makes it sound like something mysterious and intellectual.

Counterfactual thinking is post factum "what if?" type of analysis. But Bell theorem is not talking about reality, but about hypothetical models (of reality) instead that could explain entanglement and satisfy locality assumption. And obviously any scientific model represents ante factum "what if?" type of analysis (as it has to make predictions). So claiming that Bell theorem assumes 'counterfactual definiteness' is just red herring.

 

[Lord Jestocost]

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.

Regarding the term "local realism" in conjunction with Bell's theorem it might be of interest to have a look at Travis Norsen's paper "Against ‘Realism’ " (https://arxiv.org/abs/quant-ph/0607057).