CFD - Counterfactual Definiteness

[Zafa Pi]

Within QM theory if each of Alice and Bob are measuring one of a pair of entangled photons (from say √½(|00⟩ + |11⟩)) then each are observing a ±1 valued random variable with prob 1 = prob-1 = ½, irrespective of their observables (settings). These two r.v.s can range from independent to completely correlated depending on A and B's settings. That is all I understand.
If you think it is reasonable to ask whether Bob's setting has an affect on what Alice observes please propose a coherent method of how one could tell. For example, if A and B both choose the same setting then they will both observe the same value (1 or -1). Does that mean B's setting affects what Alice sees (and vise versa)?
A definition of "affect" here would be helpful. Does Alice like what she sees depending on Bob's setting?

Locality and CFD together are (is?) sufficient to prove a Bell inequality, which in turn can be contradicted by experiment. I'm not sure what more you're after. ("you" refers to anybody on this thread)

 

[morrobay]

1. Predictions for spin 1/2 pairs with Aa and Bb settings in xy plane for P++ = P-- is 1/2 (sin θ/2)²
With given settings above in setup change Aa to Aa' orientation and calculate prediction with a' - b = θ'
2. Now do experiment with Aa' setting and given Bb setting above
3. If experimental results for P++ and P-- match prediction for settings Aa' and Bb . θ', then there was no influence at Bb when setting change was made at Aa to Aa'

 

[Eye_in_the_Sky]

Well, concerning quantum phenomena, that's what we would say, yes. Retrocausal advocates argue otherwise. They have a so-called “interventionist” account of causality. See the Insight https://www.physicsforums.com/insights/retrocausality/

Thank you, for that, RUTA. I think I will have some more questions to ask you about RBW and the adynamical approach. ... But, in the mean time, I have a different sort of question on my mind and I am wondering what your opinion is.

Do you consider the statement below to be axiomatically true (where "the theory in question" can be any consistent theory 'about' the phenomenon)?

If Bob's setting is IRRELEVANT to Alice's outcome, and if the theory in question is CORRECT in this regard, then:

No contradiction can arise in the theory by supposing that Alice's outcome for (the hypothetical setting) b₂ would have been the same as that for (the actual setting) b₁.

 

[RUTA]

Thank you, for that, RUTA. I think I will have some more questions to ask you about RBW and the adynamical approach. ... But, in the mean time, I have a different sort of question on my mind and I am wondering what your opinion is.

Do you consider the statement below to be axiomatically true (where "the theory in question" can be any consistent theory 'about' the phenomenon)?

If Bob's setting is IRRELEVANT to Alice's outcome, and if the theory in question is CORRECT in this regard, then:

No contradiction can arise in the theory by supposing that Alice's outcome for (the hypothetical setting) b₂ would have been the same as that for (the actual setting) b₁.

I agree with Dr. Chinese (who is an expert in this area) -- Bob's setting is relevant to Alice's outcome in the sense that the Bell-inequality violating correlations obtain.

 

[Eye_in_the_Sky]

I agree with Dr. Chinese (who is an expert in this area) -- Bob's setting is relevant to Alice's outcome in the sense that the Bell-inequality violating correlations obtain.

Okay. Nobody knows what I'm talking about with that. So, I'll just explain what I'm trying to accomplish with it.

I am trying to resolve the dispute below.
_________

All Bell shows is if you want to have properties when not observed you need non local influences.

I agree with it (except for the usage of "All" and "is" in the sentence).

Do you agree that the following statement is also true?

[All] Bell shows [is] if you want the joint-state of Alice's ((macroscopic) measuring) instrument and Bob's ((macroscopic) measuring) instrument, in spacetime, to be separable then you need non-local influences.

No.

Its just a creelation. Thats it, that's all.

_________

SUMMARY:

Bhobba contends that the quantum correlations are compatible with both of these conditions taken together:

1) The joint state of Alice's measuring instrument and Bob's measuring instrument, in spacetime, is separable.

2) Their measuring instruments are mutually non-influencing.

I am saying that (at least) one of these conditions needs to be relinquished.
________________

Can anyone resolve this dispute? If not, can you make some helpful remarks about it?

 

[Eye_in_the_Sky]

The 'state of affairs' relevant to the outcome at A is independent of the setting at B.

OK - without getting too bogged down with the precise meaning of 'state of affairs' let us assume that this statement is false.

In other words, it is assumed there is some 'state of affairs' that is 'relevant' to the outcome at A that can be changed by a change of setting at B.

But what does 'relevant' mean? It can only mean that there is some measurable consequence - if there were no such consequence (no measureable change in the actual pings or dings) then in what sense would one actually describe it as 'relevant' to an outcome?

Consider spin-½ singlet.

Suppose Bob measures S_x and obtains the result q, where q is one of "UP" or "DOWN". Then the 'state of affairs' relevant to Alice's outcome is such that

if Alice measures S_x she cannot obtain q.

On the other hand, if Bob had measured S_y instead, then (no matter what the outcome of Bob) the 'state of affairs' relevant to Alice's outcome would have been such that

if Alice measures S_x she can obtain q.
_______

Simon – and anyone else who would like to comment – in your eyes, does the above example demonstrate 'relevance'?

 

[N88]

Okay. Nobody knows what I'm talking about with that. So, I'll just explain what I'm trying to accomplish with it.

I am trying to resolve the dispute below.
__________________

SUMMARY:

Bhobba contends that the quantum correlations are compatible with both of these conditions taken together:

1) The joint state of Alice's measuring instrument and Bob's measuring instrument, in spacetime, is separable.

2) Their measuring instruments are mutually non-influencing.

I am saying that (at least) one of these conditions needs to be relinquished.
________________

Can anyone resolve this dispute? If not, can you make some helpful remarks about it?

HTH; it's all about correlations:

Under EPRB (Bell 1964), let a and b be the orientations of the principal axes of Alice's device and Bob's device in 3-space, respectively. Then the orientation of their respective output channels is ±a and ±b, and the corresponding results are A^± and B^±.

1. Under Einstein-locality, their devices are mutually non-influencing: the state of Alice's device D(a) is independent of Bob's device D(b).

2. BUT their devices are correlated by the function: C[D(a), D(b)] = cos(a,b). When (a,b) = 0, C = 1 and the devices are parallel; when (a,b) = π/2, C= 0 and the devices are orthogonal; when (a,b) = π, C = -1 and the devices are antiparallel; etc. So their output channels are also correlated.

3. Now, let each particle pair be anti-correlated via the pairwise conservation of total angular momentum; ie, the λ heading toward Alice is the opposite of the λ heading toward Bob.

4. No surprise then that the correlation-based expectation <AB> should equal - a.b.

 

[N88]

The 'state of affairs' relevant to the outcome at A is independent of the setting at B.Consider spin-½ singlet.

Suppose Bob measures S_x and obtains the result q, where q is one of "UP" or "DOWN". Then the 'state of affairs' relevant to Alice's outcome is such that

if Alice measures S_x she cannot obtain q.

On the other hand, if Bob had measured S_y instead, then (no matter what the outcome of Bob) the 'state of affairs' relevant to Alice's outcome would have been such that

if Alice measures S_x she can obtain q.
_______

Simon – and anyone else who would like to comment – in your eyes, does the above example demonstrate 'relevance'?

Caution required: Alice cannot ever obtain S_x = q from the particle that paired with the particle from which Bob obtained S_x = q. The probability that she obtains q in the second example (Alice measures S_x; Bob measures S_y on a new particle-pair and gets ±q) is well-known.

 

[RUTA]

Okay. Nobody knows what I'm talking about with that. So, I'll just explain what I'm trying to accomplish with it.

I am trying to resolve the dispute below.

SUMMARY:

Bhobba contends that the quantum correlations are compatible with both of these conditions taken together:

1) The joint state of Alice's measuring instrument and Bob's measuring instrument, in spacetime, is separable.

2) Their measuring instruments are mutually non-influencing.

I am saying that (at least) one of these conditions needs to be relinquished.
________________

Can anyone resolve this dispute? If not, can you make some helpful remarks about it?

Both 1 and 2 are correct because the measuring devices obey classical (non-quantum) physics. To understand what's happening in that classical context with the outcomes of the quantum experiment, you need an interpretation of QM.

 

[Eye_in_the_Sky]

Both 1 and 2 are correct because the measuring devices obey classical (non-quantum) physics. To understand what's happening in that classical context with the outcomes of the quantum experiment, you need an interpretation of QM.

If you say that both 1 and 2 together are compatible with the quantum correlations, then you must also be saying that the following implication is NOT a property of spacetime:

separable & mutually non-influencing → IRRELEVANCE .

Am I right about that, RUTA? By your reckoning this is NOT a property of spacetime.
________

Here are the meanings of the terms I am using:

separable: the joint-state of Alice's measuring instrument and Bob's measuring instrument, in spacetime, is separable

mutually non-influencing: each one's instrument is uninfluenced by that of the other

IRRELEVANCE: each one's setting is IRRELEVANT to the other's outcome

 

[RUTA]

If you say that both 1 and 2 together are compatible with the quantum correlations, then you must also be saying that the following implication is NOT a property of spacetime:

separable & mutually non-influencing → IRRELEVANCE .

Am I right about that, RUTA? By your reckoning this is NOT a property of spacetime.
________

Here are the meanings of the terms I am using:

separable: the joint-state of Alice's measuring instrument and Bob's measuring instrument, in spacetime, is separable

mutually non-influencing: each one's instrument is uninfluenced by that of the other

IRRELEVANCE: each one's setting is IRRELEVANT to the other's outcome

You're trying to conflate outcomes in the measuring devices with whatever quantum system is responsible for those outcomes. Essentially at that point you're trying to make the measuring devices quantum in nature.

 

[Eye_in_the_Sky]

You're trying to conflate outcomes in the measuring devices with whatever quantum system is responsible for those outcomes. Essentially at that point you're trying to make the measuring devices quantum in nature.

You didn't answer my question.

The IMPLEMENTATION of a setting and the REGISTRATION of an outcome:
- each is an EVENT in spacetime
- each is part of the STATE-description of the instrument

So please, answer my question.

"YES" or "NO"? Is the implication below a property of spacetime?

separable & mutually non-influencing → IRRELEVANCE
________

Here, again, are the meanings of the terms I am using:

separable: the joint-state of Alice's measuring instrument and Bob's measuring instrument, in spacetime, is separable

mutually non-influencing: each one's instrument is uninfluenced by that of the other

IRRELEVANCE: each one's setting is IRRELEVANT to the other's outcome

 

[RUTA]

You didn't answer my question.

The IMPLEMENTATION of a setting and the REGISTRATION of an outcome:
- each is an EVENT in spacetime
- each is part of the STATE-description of the instrument

So please, answer my question.

"YES" or "NO"? Is the implication below a property of spacetime?

separable & mutually non-influencing → IRRELEVANCE
________

Here, again, are the meanings of the terms I am using:

separable: the joint-state of Alice's measuring instrument and Bob's measuring instrument, in spacetime, is separable

mutually non-influencing: each one's instrument is uninfluenced by that of the other

IRRELEVANCE: each one's setting is IRRELEVANT to the other's outcome

You keep talking about the measuring devices as if they're in a quantum (unobserved) state. In that case, you need an interpretation of QM to answer questions about their status in spacetime.

 

[Eye_in_the_Sky]

You keep talking about the measuring devices as if they're in a quantum (unobserved) state. In that case, you need an interpretation of QM to answer questions about their status in spacetime.

Hi, RUTA. I was digging through my old notes on my computer and came upon something which might prove helpful. It's a post of yours from some six years ago, and here's the part I'm quoting:

In today’s terminology we would say that the spacetime picture of relativity adheres to the following principles (Howard, 1997, pp 124-125):

Separability principle: any two systems A and B, regardless of the history of their interactions, separated by a non-null spatiotemporal interval have their own independent real states such that the joint state is completely determined by the independent states.

Locality principle: any two space-like separated systems A and B are such that the separate real state of A let us say, cannot be influenced by events in the neighborhood of B.

It is now generally believed that Einstein-Podolsky-Rosen (EPR) correlations, i.e., correlated space-like separated experimental outcomes which violate Bell’s inequality, force us to abandon either the separability or locality principle.

Here is the link:
https://www.physicsforums.com/threa...t-and.369328/page-28#post-2753865#post2753865
_______

From what you are saying here and now in this thread, it sounds like the belief you mentioned back then is no longer accepted. Even stronger than that, it sounds like you are saying the belief is demonstrably false. If so, what is the demonstration?

 

[Simon Phoenix]

Simon – and anyone else who would like to comment – in your eyes, does the above example demonstrate 'relevance'?

Well in this reasoning you're assuming a definite temporal order for the measurement events of Alice and Bob. But it's kind of the point of Bell experiments that the measurement events are spacelike separated (if they were not we would not able to rule out local hidden variable theories).

If the measurement events are spacelike separated then there exist frames of reference for which the events occur in the reverse order.

So is it Bob influencing Alice's 'state of affairs', or vice versa?

 

[entropy1]

I'm probably dead wrong, but this is my take on it for now:

Suppose Bob has setting b1, and Alice gets a series of outcomes S. Now suppose that if Bob had had setting b2, Alice would have got the same series of outcomes S. Then, since the correlation has changed (due to the changed settings of Bob), and Alice's outcomes are the same, Bob's outcomes must have changed. And this goes vice versa for Alice. So, this would mean that Alice's outcomes would only depend on her settings, and similarly for Bob. But then there would be no correlation dependent on the relative (!) parameters (it would be local). So, I suppose then that Bob's setting does influence the outcomes of Alice (and vice-versa). It just happens in a way that it is not noticed (locally)!

*hiding under a stone*

 

[zonde]

If the measurement events are spacelike separated then there exist frames of reference for which the events occur in the reverse order.

So is it Bob influencing Alice's 'state of affairs', or vice versa?

In Relativity simultaneity is only convention. There are no physical consequences for simultaneity because there are no FTL phenomena. If you speculate about FTL phenomena there are physical consequences for simultaneity and it can't be just convention. So it's outside of domain of applicability for Relativity.

 

[RUTA]

Hi, RUTA. I was digging through my old notes on my computer and came upon something which might prove helpful. It's a post of yours from some six years ago, and here's the part I'm quoting:

Here is the link:
https://www.physicsforums.com/threa...t-and.369328/page-28#post-2753865#post2753865
_______

From what you are saying here and now in this thread, it sounds like the belief you mentioned back then is no longer accepted. Even stronger than that, it sounds like you are saying the belief is demonstrably false. If so, what is the demonstration?

The measuring devices satisfy both principles, but the quantum systems responsible for the Bell-inequality violations do not.

 

[Eye_in_the_Sky]

You're trying to conflate outcomes in the measuring devices with whatever quantum system is responsible for those outcomes. Essentially at that point you're trying to make the measuring devices quantum in nature.

Can we, at least, agree on this much?

If one says there is no violation of 'causal locality', then one is forced to say that the PAIR of spacetime events – i.e. the IMPLEMENTATION of Bob's setting and the REGISTRATION of Alice's outcome – is 'nonseparably connected'.

 

[Eye_in_the_Sky]

Within QM theory if each of Alice and Bob are measuring one of a pair of entangled photons (from say √½(|00⟩ + |11⟩)) then each are observing a ±1 valued random variable with prob 1 = prob-1 = ½, irrespective of their observables (settings). These two r.v.s can range from independent to completely correlated depending on A and B's settings. That is all I understand.

Excellent! Me too.

All of the rest of the matter for me is mired by the poor diction and the fuzzy and entangled concepts with which we-all have fallen into using in our discussions of this topic.

A definition of "affect" here would be helpful.

If you think it is reasonable to ask whether Bob's setting has an affect ...

I have paused the statement at the word "affect"; it is a verb. The correct word is "effect"; it is a noun. I will define them both as follows:

effect: a 'state of affairs' that is brought about by a 'cause'

affect: to act, in a manner of 'causation', so as to produce an 'effect'

I will also define three more words:

influence: the agency through which an 'effect' is established

causation: the relationship between 'cause' and 'effect'

causality: the notion of 'causation'

 

[RUTA]

Can we, at least, agree on this much?

If one says there is no violation of 'causal locality', then one is forced to say that the PAIR of spacetime events – i.e. the IMPLEMENTATION of Bob's setting and the REGISTRATION of Alice's outcome – is 'nonseparably connected'.

Again, without specifying a particular QM interpretation, I would say the two outcomes are nonseparable if they are locally causal.

 

[Eye_in_the_Sky]

Again, without specifying a particular QM interpretation, I would say the two outcomes are nonseparable if they are locally causal.

Okay. I will recast my claim as follows:

A joint-measurement of an (appropriately prepared) entangled property is performed in spacetime regions A and B at spacelike separation.

If one says there is no violation of 'causal locality', then one is forced to say:

The 'state of affairs' in spacetime region A and the 'state of affairs' in spacetime region B are together in a condition of 'nonseparability'.

 

[RUTA]

Okay. I will recast my claim as follows:

A joint-measurement of an (appropriately prepared) entangled property is performed in spacetime regions A and B at spacelike separation.

If one says there is no violation of 'causal locality', then one is forced to say:

The 'state of affairs' in spacetime region A and the 'state of affairs' in spacetime region B are together in a condition of 'nonseparability'.

If by "state of affairs" you're referring to the device settings and experimental outcomes, then yes.

 

[Simon Phoenix]

In Relativity simultaneity is only convention

How so?

Let's imagine the classic train scenario. Alice is placed in the centre of a train carriage. Unfortunately for our hapless heroine, some dastardly criminal has strapped an explosive device to her. There is a light source at each end of the carriage. If the light from these sources reaches her at the same time as judged by the photodetectors on the explosive device - then it's goodbye Alice.

Bob, sitting on the embankment, watches the train go past and sees flashes from the end of the carriage that are simultaneous (by his reckoning) just as Alice passes him.

So does our heroine survive, or is she blown to bits?

I suspect Alice and Bob are going to view 'simultaneity' as something a little more serious than merely 'convention'

So it's outside of domain of applicability for Relativity

Again, how so?

The measurements of Alice and Bob are merely 2 events in spacetime. It doesn't matter one jot whether these events are measurements on entangled particles or measurements of the colour of the eyes on two fluffy bunnies. The events don't even have to be measurements of any kind - just two points in spacetime where something could happen, in fact.

What you seem to be saying is that relativity is not applicable for all possible events at these spacetime locations.

If there is a spacelike interval separating these two events, then it is possible that there are different orderings for the events in different frames.

So how can we say which event 'influences' the other when we talk of entanglement?

 

[zonde]

If the light from these sources reaches her at the same time as judged by the photodetectors on the explosive device - then it's goodbye Alice.

Bob, sitting on the embankment, watches the train go past and sees flashes from the end of the carriage that are simultaneous (by his reckoning) just as Alice passes him.

So does our heroine survive, or is she blown to bits?

I suspect Alice and Bob are going to view 'simultaneity' as something a little more serious than merely 'convention'

We can use word "simultaneously" in two different ways. We can describe single spacetime event (light pulses arrive at the same time at some place) or we can describe two distant spacetime events (light pulses are emitted at the same time from separate sources). If we describe single spacetime event then of course it's physical fact and has nothing to do with any convention.

Again, how so?

The measurements of Alice and Bob are merely 2 events in spacetime. It doesn't matter one jot whether these events are measurements on entangled particles or measurements of the colour of the eyes on two fluffy bunnies. The events don't even have to be measurements of any kind - just two points in spacetime where something could happen, in fact.

What you seem to be saying is that relativity is not applicable for all possible events at these spacetime locations.

Points in spacetime diagram by themselves represent physical facts and it has little to do with what I'm saying.

If there is a spacelike interval separating these two events, then it is possible that there are different orderings for the events in different frames.

Inconsistent orderings of spacetime events in different reference frames is a feature of relativity. It's fine (and very convenient) as long as there is no FTL phenomena.

 

[Simon Phoenix]

We can use word "simultaneously" in two different ways

We can use the word "simultaneously" however we like, but there is only one meaning in physics really. Two events are said to be simultaneous in a given inertial reference frame if they have the same time coordinate in that frame.

Simultaneity is relative, if this is what you mean by a matter of 'convention' then I agree. I would not personally describe it as a 'convention' though.

Some authors have even suggested that in fact one could even go so far as to suggest that all of special relativity is really a study of the relativity of simultaneity - not sure I'd fully agree with that statement, but I can see where they're coming from, so to speak.

Inconsistent orderings of spacetime events in different reference frames is a feature of relativity. It's fine (and very convenient) as long as there is no FTL phenomena.

So let me try to understand what you're saying.

Experiment 1 : our Alice and Bob make spacelike separated measurements on two particles. These particles are just prepared in random states with no correlation or entanglement whatsoever

Experiment 2 : same as above but now with entangled particles

Are you suggesting, somehow, that special relativity is applicable in the first experiment (so we're entitled to say that the order of measurement can differ in differing frames), but not in the second because we're now making measurements of entangled particles?

Or are you suggesting that entanglement (and maybe the Bohm view of things) invalidates special relativity?

 

[zonde]

So let me try to understand what you're saying.

Experiment 1 : our Alice and Bob make spacelike separated measurements on two particles. These particles are just prepared in random states with no correlation or entanglement whatsoever

Experiment 2 : same as above but now with entangled particles

Are you suggesting, somehow, that special relativity is applicable in the first experiment (so we're entitled to say that the order of measurement can differ in differing frames), but not in the second because we're now making measurements of entangled particles?

You might say so. Basically relativity is applicable in both cases as long as we describe our observations phenomenologically and do not speculate about possible physical models behind entanglement.

Or are you suggesting that entanglement (and maybe the Bohm view of things) invalidates special relativity?

Sort of yes, but I would rather say that entanglement phenomena (violation of Bell inequalities) indicates that domain of applicability of relativity is limited.

 

[Eye_in_the_Sky]

Suppose Bob has setting b1, and Alice gets a series of outcomes S. Now suppose that if Bob had had setting b2, Alice would have got the same series of outcomes S. Then, since the correlation has changed (due to the changed settings of Bob), and Alice's outcomes are the same, Bob's outcomes must have changed. And this goes vice versa for Alice. So, this would mean that Alice's outcomes would only depend on her settings, and similarly for Bob. But then there would be no correlation dependent on the relative (!) parameters (it would be local). So, I suppose then that Bob's setting does influence the outcomes of Alice (and vice-versa). It just happens in a way that it is not noticed (locally)!

Hi, entropy1. Thanks for contributing to this thread.

There is a difficulty with the above argument. The argument, as it stands, would apply equally well to a 'classical' correlation experiment. ... But, even there, there can be "correlation dependence" on the "relative parameters".

So, how can we clarify the matter? One way, is to do a step-by-step deconstruction of the full Bell argument in this context. Another way, is to choose a different entanglement scenario altogether, a much SIMPLER one, and pose our queries upon that background instead.

"Ah," you might ask, "there is a SIMPLER entanglement scenario I can consider?"

The answer is YES. And thus, I have started a new thread entitled:

"Bell made Simple - HARDY".

 

[Eye_in_the_Sky]

If one says there is no violation of 'causal locality', then one is forced to say:

The 'state of affairs' in spacetime region A and the 'state of affairs' in spacetime region B are together in a condition of 'nonseparability'.

If by "state of affairs" you're referring to the device settings and experimental outcomes, then yes.

Absolutely, the 'state of affairs' would include those.
________

You keep talking about the measuring devices as if they're in a quantum (unobserved) state. In that case, you need an interpretation of QM to answer questions about their status in spacetime.

Consider an inertial frame of reference in which the pair of outcomes occurs simultaneously, and let t_o be the time of occurrence in that frame.

Suppose there is no violation of 'causal locality', and suppose further that the joint-state of their instruments is 'separable' both before and after t_o.

But at t_o:

Each one's outcome is 'nonseparable' from the setting of the other; therefore, the joint-state of their instruments is 'nonseparable'.

... Is that wrong to say?

 

[RUTA]

Absolutely, the 'state of affairs' would include those.
________

Consider an inertial frame of reference in which the pair of outcomes occurs simultaneously, and let t_o be the time of occurrence in that frame.

Suppose there is no violation of 'causal locality', and suppose further that the joint-state of their instruments is 'separable' both before and after t_o.

But at t_o:

Each one's outcome is 'nonseparable' from the setting of the other; therefore, the joint-state of their instruments is 'nonseparable'.

... Is that wrong to say?

Now you're talking about the "state of the instruments," being "nonseparable" so I assume you're talking about the instruments in terms of being in a quantum state. I don't know what else you mean. If so, you need an interpretation of QM to discuss the situation ontologically because you have to deal with the measurement problem.

 

[Eye_in_the_Sky]

Now you're talking about the "state of the instruments," being "nonseparable" so I assume you're talking about the instruments in terms of being in a quantum state. I don't know what else you mean. If so, you need an interpretation of QM to discuss the situation ontologically because you have to deal with the measurement problem.

I may be having a conceptual difficulty.

To my understanding, the following conjunction is not logically possible:

each one's outcome is 'nonseparable' from the setting of the other

AND

the joint-state of their instruments is 'separable' .

Is that logically possible? ... for both statements to hold?

 

[bhobba]

each one's outcome is 'nonseparable' from the setting of the other
the joint-state of their instruments is 'separable' .

You are making it all way harder than it really is.

All Bell is saying is if you want the outcomes of measurements to be independent of the measurement then you need FTL.

The following CAREFULLY explains the issues and terms:
http://www.johnboccio.com/research/quantum/notes/paper.pdf

Thanks
Bill

 

[Simon Phoenix]

Each one's outcome is 'nonseparable' from the setting of the other; therefore, the joint-state of their instruments is 'nonseparable'.

Eye,

I've no idea where you're going with all of this and I think you're making things more complicated than they need to be.

Let's backpedal a bit and think about what the Bell analysis is all about. Let's pretend that QM hasn't been invented yet. We know nothing about 'separable' or 'non-separable' or 'wavefunctions'.

Now we have some experiment consisting of 2 pieces of measuring kit and some source. So in the usual fashion we arrange them like so
A <---------- S ----------> B
We can adjust the dial on the kit to measure at settings a,b, or c.
The outcome is just a single binary value 1 or 0 (a ping or a ding)

Everything is at 'black box' level. The only data we can record at each measuring station, for each timeslot, is the setting (a,b, or c) and the binary value obtained.

Our job is to see whether any correlations that might be observed can be explained at this very general level in terms of probability distributions that can actually be measured in this experiment.

So we quite naturally make the assumption that whatever the source is doing or generating (fields, particles, little green tribbles, etc) there are going to be some variables that will explain any correlation. We might not have any control of or access to these variables, but we assume they are underlying things and giving rise to the correlation. Furthermore we quite naturally assume that these variables are such that they have some existence independent of the measurement.

Now, it would be strange if A and B were miles apart and the results (the ping or ding) recorded at A depended in some way on the position of the dial (a,b or c) that had been chosen at B.

Let's call these kinds of variables 'classical-like' - they have properties that are very natural and reasonable. They exist outside of measurement, for one, and they don't bugger up relativity.

Now we write down the various conditional probabilities we have, do some manipulations, and find that there's a constraint on certain functions that can actually be measured in this experiment. So we know that ANY theory that utilises these kinds of variables must give predictions within these constraints.

We do the experiment and find that the results we get don't satisfy this constraint. So whatever is happening (fields, particles or tribbles) it cannot be described by a theory of this kind using these kinds of classical-like variables.

As soon as you want to try to describe things in terms of variables that have some existence independent of measurement (like everyday classical variables such as position or momentum or field strength and so on) then if you want to explain the observed results those variables have to have some non-local connection - crudely put, there must be some mechanism that transfers 'information' about settings at A to the system (kit plus tribble) at B in a way that buggers up relativity. You can't actually communicate FTL, in the sense that A and B can't use this to exchange information, but quite clearly real information about whether A has chosen a,b or c must be, in some sense 'accessible' to the kit plus tribble at B if we want to have our variables have some meaning independent of experiment.

So when you talk of the kit being 'non-separable' are you trying to understand things in terms of variables that have some objective existence outside of measurement and using 'non-separable' to describe this necessary 'information transfer mechanism'? Or do you mean something more akin to the non-separability described by QM?

 

[Simon Phoenix]

Each one's outcome is 'nonseparable' from the setting of the other; therefore, the joint-state of their instruments is 'nonseparable'.

Let's look at this from the QM perspective,

We'll model the experimental kit, the measuring devices, as quantum objects. The initial state of the correlated particles plus measuring devices is then given by

[ |10> + |01> ] ⊗ |A_initial> |B_initial>

where I'm ignoring normalization. So the particles are entangled, but the measuring devices are uncorrelated (and separable). They're not correlated to one another and nor are they correlated with the particles we're going to measure.

After the particles have interacted with the devices, but before the measurement is performed, the state evolves to

|10> |A₁>|B₀> + |01> |A₀>|B₁>

So the state of the particles plus measuring devices is entangled (or non-separable in the QM sense).

The state of the measuring devices alone is given by the density operator (non-normalized)

ρ = |A₁, B₀><A₁, B₀| + |A₀, B₁><A₀, B₁|

which is a correlated but not entangled state

So once the particles have interacted with the devices (but before the measurement) we can't 'separate' the particles plus devices.

You're trying to draw some conclusions about the measuring devices alone, in terms of non-separability, but that's not going to work within the QM picture of things.

I'm just repeating what RUTA has been trying to tell you using the QM formalism.

 

[RUTA]

I may be having a conceptual difficulty.

To my understanding, the following conjunction is not logically possible:

each one's outcome is 'nonseparable' from the setting of the other

AND

the joint-state of their instruments is 'separable' .

Is that logically possible? ... for both statements to hold?

Yes, the instruments are classical but the outcomes they register are described by a quantum state that depends on the settings of those instruments in nonseparable (assuming causal locality) fashion.