Bohr's solution to the EPR paradox

[PGaccount]

First, I will give my understanding of Bohr's resolution using an example that Bohr considers in his discussion. Then I will quote a passage where Bohr summarizes his resolution of the paradox. Finally, I will try to respond to John Bell's comments on this resolution. I would be interested in hearing your opinions and comments about what I say.

Consider a diaphragm with a slit, through which a particle passes. Say we have measured the momentum of the diaphragm before the passage of the particle. Now, once the particle has passed through the slit, we are free either to repeat the momentum measurement, or to measure the position of the diaphragm. So, without disturbing the particle which has already passed through the slit, we can predict either its initial position or its momentum. Einstein concludes from this that both the initial position and its momentum must be real properties of the system. Bohr argues that the possible types of predictions regarding the future behavior of the particle depend on what you choose to do with the diaphragm, even though you are not interfering with the particle after it has passed through the slit. The state of a particle is not an independent property of the particle itself, but is tied up with the conditions of the experiment, so you can disturb the state without interfering with the particle by influencing the conditions of the experiment.

There is in a case like that just considered no question of a mechanical disturbance of the system under investigation during the last critical stage of the measuring procedure, but even at this stage there is essentially the question of an influence on the very conditions which define the possible types of predictions regarding the future behavior of the system. Since these conditions constitute an inherent element of the description of any phenomenon to which the term "physical reality" can be properly attached, we see that the argumentation of the mentioned authors does not justify their conclusion that the quantum mechanical description is essentially incomplete. On the contrary, this description, as appears from the preceding discussion, may be characterized as a rational utilization of all possibilities of unambiguous interpretation of measurements, compatible with the finite and uncontrollable interaction between the objects and the measuring instruments in the field of quantum theory.

Some comments by John bell:

Indeed I have very little idea of what this means. I do not understand in what sense the word "mechanical" is used, in characterizing the disturbances which Bohr does not contemplate, as distinct from those that he does

I believe that Bohr simply referring to the fact that the particle which has already passed through the slit is not being interfered with.

I do not understand what the italicized passage means - "an influence on the very conditions" - could it mean that different kinds of experiments on the first system give different kinds of information about the second? But this was just one of the main points of EPR, who observed that one could learn either the position or the momentum of the second system

Here, I believe that Bohr is saying that the idea of 'state' in quantum theory ill defined without a specification of the whole experimental arrangement. Even though the particle has already passed through the slit, the meaning of 'state' is still inextricably connected to what you do to diaphragm, because that is part of the experimental procedure.

And the I do not understand the final reference to "uncontrollable interactions between measuring instruments and objects", It seems just to ignore the essential point of EPR that in the absence of action at a distance, only the first system could be supposed disturbed by the measurement

I believe the central point here, again, is that disturbing the conditions of the experiment is equivalent to a disturbance of the state, a word which cannot be applied to the second system by itself, but rather only to experimental set up as a whole. The fact that one cannot control separately or somehow take into account the effect of the measuring apparatus on the system in order to specify the state of the objects, like it was possible in classical physics, means that there is no sharp distinction between an independent 'state' of the objects and the measured interactions with the experimental setup.

 

[Zafa Pi]

First, I will give my understanding of Bohr's resolution using an example that Bohr considers in his discussion.

My brief take on the EPR paradox is: A pair of entangled, say, photons is created, one sent to Alice and the other to Bob who are far apart. A measures at 0° and gets 1, B measures at 45° and gets -1. But we know that if A measures at the same angle as B they will get the same value. Hence we conclude that we know that A's photon values at both 0° and 45°. This contradicts a basic tenet of QM (the H.U.P.).

Now Bohr said a lot of stuff that Bell said he didn't understand, and I don't understand it either. But he did say one thing I think do understand: Measurements not made do not necessarily have a value. What I think he meant in modern parlance is a rejection of CFD. The point is that EPR never measured A's photon at 45°. If A had measured at 45° instead of 0° there is no guarantee they would both get -1, that experiment was not carried out. The assumption of CFD is what allows Bell's inequality to be proved, without it there is no Bell's inequality and no EPR paradox.
There are those that disagree with me on this issue, but have not given arguments that have changed my mind.

None this may be addressing your concerns, I'm not sure.

I believe the central point here, again, is that disturbing the conditions of the experiment is equivalent to a disturbance of the state, a word which cannot be applied to the second system by itself, but rather only to experimental set up as a whole. The fact that one cannot control separately or somehow take into account the effect of the measuring apparatus on the system in order to specify the state of the objects, like it was possible in classical physics, means that there is no sharp distinction between an independent 'state' of the objects and the measured interactions with the experimental setup.

It is true that one photon from an entangled pair has no state until measured, but it seems to me that there are photons that have a well defined state independent of how they will be measured, e.g. planar horozontally polarized. What am I missing?

 

[Prathyush]

My brief take on the EPR paradox is: A pair of entangled, say, photons is created, one sent to Alice and the other to Bob who are far apart. A measures at 0° and gets 1, B measures at 45° and gets -1. But we know that if A measures at the same angle as B they will get the same value. Hence we conclude that we know that A's photon values at both 0° and 45°. This contradicts a basic tenet of QM (the H.U.P.).

This is not what what quantum mechanics is. Bohr's key point is in any given experimental situation we can only talk about the evidence obtained from that experiment. It is wrong to talk about an experiment which we have not performed. It is wrong to say we know photon's values at 0 and 45, because by construction of this experiment we are measuring the value of the spin of A at 0.

In summary what we know from the experiment you constructed for us is we know the spin of the electron A at 45 and spin of electron B at 0. That is all we can talk about.

Heisenberg uncertainty Principle(HUP), usually talks about statistics obtained from measurements performed using 2 complementary experimental arrangements. There a sense in which it can be used for a single measurement, but that is not of interest here. If you construct 2 complementary experimental arrangements and obtain statistics, you will see that HUP is not violated.

What I think he meant in modern parlance is a rejection of CFD.

What is CFD?

 

[stevendaryl]

What is CFD?

Counter-factual definiteness. That's the claim that the questions of the form "What would Alice's result have been if she had measured photon polarization along this axis?"

The odd thing about the EPR experiment is that it seems to satisfy CFD, at least for some counter-factuals. Alice finds that her photon is polarized in direction $\vec{A}$. Bob finds his photon is polarized in direction $\vec{B}$. It seems that Alice can confidently say, counterfactually, that "If Bob had measured polarization along axis $\vec{A}$ he would have found his photon had that polarization." Similarly, Bob can say "If Alice had measured polarization along axis $\vec{B}$, she would have found her photon had that polarization." That seems like a limited type of counterfactual reasoning that is supported by QM.

 

[Prathyush]

"What would Alice's result have been if she had measured photon polarization along this axis?"

That is not a question we can ask. Because the experiment has not been performed. That is all. What is relevant is what measurement did Alice do.

If Bob had measured polarization along axis $\vec{A}$ he would have found his photon had that polarization." Similarly, Bob can say "If Alice had measured polarization along axis $\vec{B}$, she would have found her photon had that polarization.

An point to note in an EPR type experiment is the observables measured by Alice and Bob commute. There is never a causality problem.

 

[stevendaryl]

That is not a question we can ask.

Sure we can. Science is all about counter-factuals. What happens if we do X? Even if X has never been done before, we can use our best scientific theories to make a prediction about what would happen if we did X. The prediction might be wrong, but we can certainly ask the question, and our theories can give an answer. If science were only applicable to what has actually be done in the past, it would be useless.

An point to note in an EPR type experiment is the observables measured by Alice and Bob commute. There is never a causality problem.

I didn't say anything about causality.

 

[stevendaryl]

Sure we can. Science is all about counter-factuals. What happens if we do X? Even if X has never been done before, we can use our best scientific theories to make a prediction about what would happen if we did X. The prediction might be wrong, but we can certainly ask the question, and our theories can give an answer. If science were only applicable to what has actually be done in the past, it would be useless.

When it comes to EPR, if Alice measured her photon's polarization relative to axis $\vec{A}$ and Bob measured his photon relative to axis $\vec{B}$, then there is a real sense that there is a definite answer to the questions "What if Alice had measured along axis $\vec{B}$?" "What if Bob had measured along axis $\vec{A}$?". CFD only fails if we ask about a third direction, $\vec{C}$.

 

[Prathyush]

Sure we can. Science is all about counter-factuals. What happens if we do X? Even if X has never been done before, we can use our best scientific theories to make a prediction about what would happen if we did

Science can make predictions when the experimental conditions are well defined.

What is your central point ? I don't know what we are discussing here.

 

[stevendaryl]

Science can make predictions when the experimental conditions are well defined.

Those predictions include counter-factual predictions. If you predict "If you do X, then you will find result Y", then that prediction is a definite prediction even if someone chooses not to do X.

What is your central point ? I don't know what we are discussing here.

You asked what CFD meant, and I was answering you.

 

[Prathyush]

Those predictions include counter-factual predictions. If you predict "If you do X, then you will find result Y", then that prediction is a definite prediction even if someone chooses not to do X.
You asked what CFD meant, and I was answering you.

Ok for clarity's sake, you agree that there is no paradox in EPR type experiments right ?

 

[stevendaryl]

Ok for clarity's sake, you agree that there is no paradox in EPR type experiments right ?

I'm not wading into that. My opinion about it is not certain enough to be worth sharing.

 

[forcefield]

Einstein must have thought that Bohr thought that there is no determinism. Hence Einstein thought that Bohr thought that the action is "spooky".

 

[Zafa Pi]

This is not what what quantum mechanics is. Bohr's key point is in any given experimental situation we can only talk about the evidence obtained from that experiment. It is wrong to talk about an experiment which we have not performed. It is wrong to say we know photon's values at 0 and 45, because by construction of this experiment we are measuring the value of the spin of A at 0.

In summary what we know from the experiment you constructed for us is we know the spin of the electron A at 45 and spin of electron B at 0. That is all we can talk about.

Though you slightly twisted my statement, this is just my interpretation of what Bohr was saying. You need to reread my 2nd paragraph in post #2.

 

[Prathyush]

Though you slightly twisted my statement, this is just my interpretation of what Bohr was saying. You need to reread my 2nd paragraph in post #2.

I actually did not quite read paragraph 2 after a point because I did not know what CFD was. If you agree with me its fine.

 

[Prathyush]

It is true that one photon from an entangled pair has no state until measured, but it seems to me that there are photons that have a well defined state independent of how they will be measured, e.g. planar horozontally polarized. What am I missing?

It would depend on what exactly we mean by the word state. In any well defined experimental scenario, quantum mechanics can be interpreted without ambiguity. In classical mechanics, there is no ambiguity in the definition of what we mean by state. It means position and momentum.(Or field variables and momentum density etc..).

In quantum mechanics the word state has a very different meaning. Planar horizontally polarized photons is equivalent to entangled photons, there is no formal difference between the two. Planar Horizontally polarized lends itself to a neat classical visualization, however entangled photons do not. That is the only difference. In quantum mechanics, when we attempt to obtain information about the photon, there is ambiguity about how this information is obtained which must be clarified through the detailed construction of the apparatus.

 

[Zafa Pi]

The odd thing about the EPR experiment is that it seems to satisfy CFD, at least for some counter-factuals. Alice finds that her photon is polarized in direction $\vec{A}$. Bob finds his photon is polarized in direction $\vec{B}$. It seems that Alice can confidently say, counterfactually, that "If Bob had measured polarization along axis $\vec{A}$ he would have found his photon had that polarization." Similarly, Bob can say "If Alice had measured polarization along axis $\vec{B}$, she would have found her photon had that polarization." That seems like a limited type of counterfactual reasoning that is supported by QM.

If I understand you correctly then I agree, but don't find it odd. QM certainly does not contradict all counterfactuals, e.g. Alice didn't pick up the leaf so it is on the ground; however if instead she had picked up the leaf it would not be on the ground. But, IMO, QM does say that CFD is not universally valid, as opposed to classical theory that says it is.

When someone who is not equipped with math or physics asks me what is it about QM that makes it so different from the old physics, this is what I give them:

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 still have had to get 0 if Bob did X instead, and thus yes, Bob must get 0 because of 2).
This type of reasoning leads to conclusions (e.g. something called Bell's inequality) that are contradicted by QM and experiment.

I would like to hear your opinion of this?
BTW, if 4) had read "If Bob had performed X instead of Y would he necessarily agree with Alice?" then the QM answer would be yes as well, and thus confirming your statement above.

 

[Zafa Pi]

Planar horizontally polarized photons is equivalent to entangled photons, there is no formal difference between the two.

A planar horizontally polarized photon has state |0⟩ in q-computation notation. I don't understand what you're saying, or if I do then I disagree. They are prepared in entirely different ways.

 

[Prathyush]

It is true that one photon from an entangled pair has no state until measured, but it seems to me that there are photons that have a well defined state independent of how they will be measured, e.g. planar horozontally polarized. What am I missing?

A planar horizontally polarized photon has state |0⟩ in q-computation notation. I don't understand what you're saying, or if I do then I disagree. They are prepared in entirely different ways.

I mean to say that they are equally well defined.

 

[PeterDonis]

Science is all about counter-factuals. What happens if we do X?

You're conflating two different meanings of "counterfactual". Asking "what happens if we do X?", if we haven't yet run the experiment at all, is a question about the future; it's only counterfactual in the sense that the future hasn't happened yet. As I understand Bohr's position, he wasn't talking about this type of counterfactual at all.

Asking "what would have happened if we did X?" after we have already run the experiment and done Y, is counterfactual in a different sense: it's asking about something that has already happened, but happened in a different way than the way we are asking about. As I understand Bohr's position, he was only talking about the latter type of counterfactual, and saying that it was not meaningful.

 

[stevendaryl]

You're conflating two different meanings of "counterfactual". Asking "what happens if we do X?", if we haven't yet run the experiment at all, is a question about the future; it's only counterfactual in the sense that the future hasn't happened yet. As I understand Bohr's position, he wasn't talking about this type of counterfactual at all.

But if you make a definite prediction along the lines of "If you do X,then Y will happen." and you don't do X, then it becomes a counterfactual.

 

[PeterDonis]

if you make a definite prediction along the lines of "If you do X,then Y will happen." and you don't do X, then it becomes a counterfactual.

I would say it becomes a failure to test your prediction.

 

[Zafa Pi]

I mean to say that they are equally well defined.

Huh? A single photon from an entangled pair has no state; a photon with state |0⟩ has a state.

 

[Prathyush]

Huh? A single photon from an entangled pair has no state; a photon with state |0⟩ has a state.

The entangle pair has a state, and both the photons together consist of the system. So you cannot talk about state of an individual photon when they are entangled.

 

[Zafa Pi]

As I understand Bohr's position, he was only talking about the latter type of counterfactual, and saying that it was not meaningful.

Wow, I agree with you; what's going on? However, I wouldn't have used the words "not meaningful", but rather "not valid".

 

[ueit]

When someone who is not equipped with math or physics asks me what is it about QM that makes it so different from the old physics, this is what I give them:

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 still have had to get 0 if Bob did X instead, and thus yes, Bob must get 0 because of 2).
This type of reasoning leads to conclusions (e.g. something called Bell's inequality) that are contradicted by QM and experiment.

1. What is the specific classical theory you have in mind when reaching the above conclusion?
2. Are there any calculations backing this up or it's just your intuition?

Andrei

 

[stevendaryl]

The entangle pair has a state, and both the photons together consist of the system. So you cannot talk about state of an individual photon when they are entangled.

I think that's what @Zafa Pi meant when he said "A single photon from an entangled pair has no state". Or are you making a distinction between "It has no state" and "It has a state, but you cannot talk about it"?

 

[Prathyush]

I think that's what @Zafa Pi meant when he said "A single photon from an entangled pair has no state". Or are you making a distinction between "It has no state" and "It has a state, but you cannot talk about it"?

I am saying an entangled pair is a well defined state.

 

[N88]

If I understand you correctly then I agree, but don't find it odd. QM certainly does not contradict all counterfactuals, e.g. Alice didn't pick up the leaf so it is on the ground; however if instead she had picked up the leaf it would not be on the ground. But, IMO, QM does say that CFD is not universally valid, as opposed to classical theory that says it is.

When someone who is not equipped with math or physics asks me what is it about QM that makes it so different from the old physics, this is what I give them:

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. [My emphsasis.]

With classical physics we know that the reality facing Alice is unaffected by what Bob does, so she would still have had to get 0 if Bob did X instead, and thus yes, Bob must get 0 because of 2).
This type of reasoning leads to conclusions (e.g. something called Bell's inequality) that are contradicted by QM and experiment.

I would like to hear your opinion of this?
BTW, if 4) had read "If Bob had performed X instead of Y would he necessarily agree with Alice?" then the QM answer would be yes as well, and thus confirming your statement above.

Please: On what basis do you claim: Classical physics says yes and quantum physics says no. ??

 

[Zafa Pi]

When someone who is not equipped with math or physics asks me what is it about QM that makes it so different from the old physics, this is what I give them:

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 still have had to get 0 if Bob did X instead, and thus yes, Bob must get 0 because of 2).
This type of reasoning leads to conclusions (e.g. something called Bell's inequality) that are contradicted by QM and experiment.

1. What is the specific classical theory you have in mind when reaching the above conclusion?
2. Are there any calculations backing this up or it's just your intuition?

Please: On what basis do you claim: Classical physics says yes and quantum physics says no. ??

Classical physics, in general, accepts local realism. If in a given experiment Alice performs experiment X and gets a value 0, then because of 1) (= locality), and due to the reality facing Alice as she does the experiment (= realism) it doesn't matter whether Bob had performed experiment X or Y. Hence if he had done X, because of 2) he must also get 0. Or, if Bob had done X he would have gotten some value b (= CFD) and because of 2) b = 0.
N.B. local realism is sufficient to derive Bell's inequality which has been shown to be experimentally false.

From the point of view of QM, the experiment that was performed was Alice doing X getting 0, while Bob doing Y getting 1. The experiment of Alice doing X while Bob doing X was not performed. Thus we cannot say that Alice would necessarily get 0 if Alice and Bob both did X.
This is exactly the objection of Bohr in the EPR "paradox" that @PeterDonis, @stevendaryl, and I were talking about in previous posts above.
[Mentor's note: This post has been gently edited to remove a bit of attempted political humor.]

 

[N88]

...

From the point of view of QM, the experiment that was performed was Alice doing X getting 0, while Bob doing Y getting 1. The experiment of Alice doing X while Bob doing X was not performed. Thus we cannot say that Alice would necessarily get 0 if Alice and Bob both did X.
This is exactly the objection of Bohr in the EPR "paradox" that @PeterDonis, @stevendaryl, and I were talking about in previous posts above.

Given Aspect (2004) http://arxiv.org/pdf/quant-ph/0402001v1.pdf we can write (via probability theory and QM):

$E(AB) = 2P(B^+|A^+) - 1 = cos 2(a,b).$ (1)

Let Alice do X (ie, set her detector-orientation to $a$), and get $A^+ = +1$ (while Bob does Y).

But IF (counterfactually) Bob had done X (ie, had set his detector-orientation to $a$), THEN:

$P(B^+|A^+) = 1.$ (2)

So Bob (had he done X) would indeed have gotten $B^+ = +1$ with certainty. QED per QM.

And we thus avoid the difficulties in understanding Bohr's response to EPR.

PS: under EPRB or Bell (1964), we would have Bob counterfactually setting his detector to $-a$ to get the same result as Alice, with certainty. We thus counter (under QM) your claim wrt an experiment not performed.

 

[PeterDonis]

So Bob (had he done X) would indeed have gotten $B^+ = +1$ with certainty.

But this only holds for the special case of Alice's and Bob's angles being exactly the same. (Or exactly opposite, in the EPR/Bell case.) There are infinitely many other possible cases, none of which your argument applies to.

The problem here appears to be that you are taking "If Bob had done X" too narrowly, possibly because that counterfactual was phrased in this thread too narrowly. It should be "If Bob had done Z", where Z is any other experimental setting that Bob could have chosen--in this case, any other angle Bob could have chosen to measure the spin at, besides the one he actually chose. A "realist" interpretation of QM, as I understand the usual interpretation of that term, would require all of those "If Bob had done Z" counterfactuals to have definite, well-defined answers, not just the particular one "If Bob had done X" in which Bob chose the exact measurement angle for which QM does happen to predict a particular result for him with certainty.

 

[Zafa Pi]

So Bob (had he done X) would indeed have gotten B+=+1B+=+1B^+ = +1 with certainty. QED per QM.

I didn't follow @PeterDonis at post#31, so I'll put in my 2cents worth.
OK, we let X be Aspect's experiment with a = b, so if Alice and Bob both do X then they will each get + or each get - with probability ½ for either case. So my 2) in post#16 is satisfied.
Alice does X and gets + while Bob times his pulse and gets 68. Now we ask what if Bob did X instead? Well that wasn't the experiment that was done. So let's do the experiment where Bob does X instead. That's a new experiment, and you say Alice will still get +. But why is that? Why not both getting -? I can tell you what a classical physicist would say (and I did), but I'm not one and don't believe in realism and neither did Bohr. I feel like I'm repeating myself; are you getting bohred?

 

[N88]

I didn't follow @PeterDonis at post#31, so I'll put in my 2cents worth.
OK, we let X be Aspect's experiment with a = b, so if Alice and Bob both do X then they will each get + or each get - with probability ½ for either case. So my 2) in post#16 is satisfied.
Alice does X and gets + while Bob times his pulse and gets 68. Now we ask what if Bob did X instead? Well that wasn't the experiment that was done. So let's do the experiment where Bob does X instead. That's a new experiment, and you say Alice will still get +. But why is that? Why not both getting -? I can tell you what a classical physicist would say (and I did), but I'm not one and don't believe in realism and neither did Bohr. I feel like I'm repeating myself; are you getting bohred?

PeterDonis' post #31 is fine with me. But there is an error in your analysis of what I wrote. I did not say: "In a new experiment Alice will still get +1."

You are right to say that they will get (with $P = \frac{1}{2}),$ +1 together of -1 together in a new experiment.

PS: Giving you a good combo of Einstein-locality and Bohr-realism, I believe in commonsense local realism (CLR), the union of local-causality (no causal influence propagates superluminally) and physical realism (some physical properties change interactively).

CLR is compatible with the principles of local realism in d’Espagnat (1979:158) and endorsed by Bell (1980:7): (i) realism = regularities in observed phenomena are caused by some physical reality whose existence is independent of human observers; (ii) locality = no influence of any kind can propagate superluminally; (iii) induction = legitimate conclusions can be drawn from consistent observations.

 

[ueit]

When someone who is not equipped with math or physics asks me what is it about QM that makes it so different from the old physics, this is what I give them:

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 still have had to get 0 if Bob did X instead, and thus yes, Bob must get 0 because of 2).
This type of reasoning leads to conclusions (e.g. something called Bell's inequality) that are contradicted by QM and experiment.Classical physics, in general, accepts local realism. If in a given experiment Alice performs experiment X and gets a value 0, then because of 1) (= locality), and due to the reality facing Alice as she does the experiment (= realism) it doesn't matter whether Bob had performed experiment X or Y. Hence if he had done X, because of 2) he must also get 0. Or, if Bob had done X he would have gotten some value b (= CFD) and because of 2) b = 0.
N.B. local realism is sufficient to derive Bell's inequality which has been shown to be experimentally false.

From the point of view of QM, the experiment that was performed was Alice doing X getting 0, while Bob doing Y getting 1. The experiment of Alice doing X while Bob doing X was not performed. Thus we cannot say that Alice would necessarily get 0 if Alice and Bob both did X.
This is exactly the objection of Bohr in the EPR "paradox" that @PeterDonis, @stevendaryl, and I were talking about in previous posts above.

In classical physics Alice's and Bob's actions as well as the properties of the particles and measurement results are uniquely determined by the initial state. If Bob does X you need an initial state, let's call it Bx. If Bob does Y you need a different initial state, say By.

In order to your above argument to hold you need to show that there exist such initial states Bx and By that only have consequences for Bob. Otherwise it might be the case that changing the initial state from Bx to By also changes what Alice is doing or the spin itself. And now it is important to say what classical theory you have in mind. If you use a theory without long-range interactions (billiard balls) finding the required initial states is trivial (you just re-position the "balls" Bob is made of). On the other hand if you use a field theory with unlimited range (classical electromagnetism for example) a change of the particles' configuration at Bob's location in the past will necessarily affect Alice as well.

Andrei

 

[DrChinese]

CLR is compatible with the principles of local realism in d’Espagnat (1979:158) and endorsed by Bell (1980:7):..

Perhaps you mean that the DEFINITION of CLR is as you describe. Certainly neither d’Espagnat nor Bell were advocates of anything like what you call CLR, since it's ruled out by Bell's Theorem.