Is Bell's Theorem a Valid Solution to the Locality Versus Nonlocality Issue?

[harrylin]

Thanks! Apparently you (and Bell?) interpret "then" as "only then"... I'll look up the original to see if it was just formulated in an awkward way. If so, "EPR reality" is much more narrow than the common concept of "reality"!

I now checked it (I downloaded it from the source but thanks for making it accessible for everyone!). It looks clear to me that your interpretation, "No element of reality if the observable cannot be predicted with certainty, according to EPR" is mistaken:

"We shall be satisfied with the following criterion [..] far from exhausting all possible ways of recognizing a physical reality [...]." and "Regarded not as a necessary, but merely a sufficient condition of reality, this criterion [...]". -EPR1935.

Thus their predictibility criterion was for them (of course!) not a necessary condition of reality. If Bell's theorem would be based on the assumption that it is a necessary condition for EPR, then his theorem would be wrong. However, I'm not aware that such is the case.

Regards,
Harald

 

[JesseM]

I now checked it (I downloaded it from the source but thanks for making it accessible for everyone!). It looks clear to me that your interpretation, "No element of reality if the observable cannot be predicted with certainty, according to EPR" is mistaken

It depends if by "no element of reality" you just mean "we are not justified in concluding there is an element of reality in that case, though there could be" or "there is definitely no element of reality in that case". I think EPR (and DrChinese, and Bell) would say the first, but not the second.

 

[harrylin]

It depends if by "no element of reality" you just mean "we are not justified in concluding there is an element of reality in that case, though there could be" or "there is definitely no element of reality in that case". I think EPR (and DrChinese, and Bell) would say the first, but not the second.

This is about what EPR meant (and with less importance what DrChinese meant); and I think that everyone meant what they wrote:

"not as a necessary, but merely a sufficient condition of reality". -EPR

Which is exactly how I understood it in post #36. Then I asked:

" Just to be sure: does EPR according to Bell also assume that if I can not predict Alice's result in advance, there may still be an element of reality? I ask as that is rather common for modern local realist theories."

To which DrChinese answered:

"No element of reality if the observable cannot be predicted with certainty, according to EPR."

Harald

 

[JesseM]

This is about what EPR meant (and with less importance what DrChinese meant); and I think that everyone meant what they wrote:

"not as a necessary, but merely a sufficient condition of reality". -EPR

Which is exactly how I understood it in post #36. Then I asked:

" Just to be sure: does EPR according to Bell also assume that if I can not predict Alice's result in advance, there may still be an element of reality? I ask as that is rather common for modern local realist theories."

To which DrChinese answered:

"No element of reality if the observable cannot be predicted with certainty, according to EPR."

Hmm, I suspect there was some miscommunication there and DrChinese thought you were just asking if according to EPR's argument we are justified in inferring an element of reality in that case. But perhaps DrChinese can comment...

 

[DrChinese]

I now checked it (I downloaded it from the source but thanks for making it accessible for everyone!). It looks clear to me that your interpretation, "No element of reality if the observable cannot be predicted with certainty, according to EPR" is mistaken:

"We shall be satisfied with the following criterion [..] far from exhausting all possible ways of recognizing a physical reality [...]." and "Regarded not as a necessary, but merely a sufficient condition of reality, this criterion [...]". -EPR1935.

Thus their predictibility criterion was for them (of course!) not a necessary condition of reality. If Bell's theorem would be based on the assumption that it is a necessary condition for EPR, then his theorem would be wrong. However, I'm not aware that such is the case.

Regards,
Harald

I said it was sufficient as a definition when I quoted it. I also said that there is no element of reality without that. I meant that per the definition in use. Perhaps you have a better definition.

Strictly speaking, it is certainly possible there is an element of reality WITHOUT us being able to predict it in advance. For example, I had to pay when my son wrecked the car even though I could not predict the amount in advance with certainty. And believe me, that was very real to my pocketbook.

So if you take the contranegative (also being true), you get: IF you cannot predict in advance with certainty, THEN there is no element of reality. But what can you do with this statement? I don't think too much, because you cannot prove the antecedent.

So my point is: Bell used the well accepted EPR definition. That definition is one which is easy to follow, and because it is sufficient it is enough for our examples. I.e. for entangled pairs. The only issue to Bell would be if you could prove convince folks that this was not a sufficient condition. That would be a tough hurdle. Keep in mind that was a cornerstone of EPR.

 

[DrChinese]

Hmm, I suspect there was some miscommunication there and DrChinese thought you were just asking if according to EPR's argument we are justified in inferring an element of reality in that case. But perhaps DrChinese can comment...

Yes, I think a slight miscommunication. Per EPR's definition, they would not have ascribed an element of reality without meeting this requirement. Not that they themselves believed as such. They simply used it for convenience. I think it was a brilliant touch, personally.

That was why I mentioned it as a sufficient condition. There could exist a less restrictive definition, I just cannot imagine such which is also useful.

 

[DrChinese]

I ask as that is rather common for modern local realist theories."

To which DrChinese answered:

"No element of reality if the observable cannot be predicted with certainty, according to EPR."

Harald

The local realist wants a MORE restrictive definition of reality, not less. That way Bell wouldn't apply. So the way you are headed (i.e. towards a lesser definition) doesn't do too much.

 

[JesseM]

So if you take the contranegative (also being true), you get: IF you cannot predict in advance with certainty, THEN there is no element of reality.

Why would that statement be true though? Let A=you can predict in advance with certainty, and B=there is an element of reality. A -> B is not logically equivalent to ~A -> ~B, so just because you believe the first there is no justification for believing the second.

 

[JesseM]

Yes, I think a slight miscommunication. Per EPR's definition, they would not have ascribed an element of reality without meeting this requirement. Not that they themselves believed as such. They simply used it for convenience. I think it was a brilliant touch, personally.

Right, if the requirement wasn't met then they wouldn't say there was any justification for believing there must be an element of reality (whereas if the requirement was met they would), but that doesn't mean they would definitely conclude there wasn't an element of reality either, they just wouldn't claim to know one way or another, and thus this scenario (where you can't predict with certainty) isn't useful to their argument. harrylin was interpreting you to mean they would say if you couldn't predict with certainty, then there is definitely no hidden element of reality that predetermines the measurement outcome, but that wouldn't be EPR's claim or Bell's.

 

[DrChinese]

Why would that statement be true though? Let A=you can predict in advance with certainty, and B=there is an element of reality. A -> B is not logically equivalent to ~A -> ~B, so just because you believe the first there is no justification for believing the second.

A-> B

implies

~B -> ~A

Too bad I reversed it.

 

[DrChinese]

Right, if the requirement wasn't met then they wouldn't say there was any justification for believing there must be an element of reality (whereas if the requirement was met they would), but that doesn't mean they would definitely conclude there wasn't an element of reality either, they just wouldn't claim to know one way or another, and thus this scenario (where you can't predict with certainty) isn't useful to their argument. harrylin was interpreting you to mean they would say if you couldn't predict with certainty, then there is definitely no hidden element of reality that predetermines the measurement outcome, but that wouldn't be EPR's claim or Bell's.

Yup. Somehow or another, he probably wants to draw some parallel to Bell tests where the angle settings lead to a fraction rather than certainty. But of course there is no connection there.

 

[JesseM]

A-> B

implies

~B -> ~A

Too bad I reversed it.

It's easy to get tripped up by these logic rules I can never keep them straight so I always have to think about examples, like A="an integer is prime and larger than 2", and B="the integer is odd"

 

[Rap]

Most scientists do not accept that there is a value to unmeasured particle observables. They reject CFD. That is mainline QM. There are the various interpretations such as MWI, BM, Copenhagen, etc. which all make the same predictions.

This is not my understanding of CFD. CFD means that, looking forward, if I can predict with 100% accuracy the outcome of a particular measurement, then I am justified in assuming, looking backward, that, not having made such a measurement, but if I had made such a measurement, it would have given the predicted results. Classically, this is so trivially true as to be not worth mentioning, but in QM, where one measurement may preclude another (e.g. measuring momentum precludes measuring position simultaneously), it needs to be examined.

In the case of Bell, you can illustrate the paradox with just one pair of measurements along with the statement "Although Alice and Bob did not align their detectors, had they aligned their detectors, they would have measured equal and opposite spins." This is an acceptance of CFD and produces the paradox. Rejecting CFD removes the paradox, and the need for superluminal effects to resolve the paradox.

 

[JesseM]

Rejecting CFD removes the paradox, and the need for superluminal effects to resolve the paradox.

But "superluminal effects" are only needed in a realistic model whose basic elements are localized "beables" (see Bell's paper The Theory of Local Beables), and predictions about experimental results are derived from the behavior of these beables. What Bell proves is that if you have such a model, there's no way to have it also be true that these local beables are only causally influenced by events in their past light cone. If you look at the definition of local realism I gave in [post=3231977]this post[/post], then the idea is that if you accept part 1) of my definition there, according to QM part 2) can't also be correct. But if you don't accept 1) in the first place, as your preference for pure QM with no hidden variables would suggest, then you're free to adopt some totally different definition of "locality" like one that just says that it's impossible to use measurements to transmit messages faster-than-light. The issue of QM being incompatible with locality only comes up when you use a definition of "locality" based on the realistic assumption that there must be a model that breaks up the state of a region at any given time into a collection of localized facts, as outlined in part 1) of my definition, and then says that causal influences between these localized facts shouldn't move faster than light.

 

[DrChinese]

This is not my understanding of CFD. CFD means that, looking forward, if I can predict with 100% accuracy the outcome of a particular measurement, then I am justified in assuming, looking backward, that, not having made such a measurement, but if I had made such a measurement, it would have given the predicted results. Classically, this is so trivially true as to be not worth mentioning, but in QM, where one measurement may preclude another (e.g. measuring momentum precludes measuring position simultaneously), it needs to be examined.

In the case of Bell, you can illustrate the paradox with just one pair of measurements along with the statement "Although Alice and Bob did not align their detectors, had they aligned their detectors, they would have measured equal and opposite spins." This is an acceptance of CFD and produces the paradox. Rejecting CFD removes the paradox, and the need for superluminal effects to resolve the paradox.

Counterfactual definteness does not require you be able to predict something in advance. That is more related to the EPR definition of elements of reality. They are related. This is certainly a classical concept regardless of where you draw the line.

The issue with Bell is quite different per your second paragraph. You don't really need the requirement that the spins be opposite. More that they have a value.

 

[yoda jedi]

Rejecting CFD removes the paradox, and the need for superluminal effects to resolve the paradox.

not necessarily, just postulating nonseparability is enough.


.

 

[yoda jedi]

"EPR reality" is much more narrow than the common concept of "reality"!

of course you are Right.
Reality is what exist, the state of things as they actually exist. "No Strings Attached".

with CFD or without CFD.


.

 

[billschnieder]

The issue with Bell is quite different per your second paragraph. You don't really need the requirement that the spins be opposite. More that they have a value.

Hidden in the highlighted phrase is a modal fallacy. A prediction MUST always be conditioned on the assumptions, ie it can not be true apart from its conditioning assumptions. For example "If Bob and Alice measure the two photons at angles b and a, they will obtain x, and y" and "If Bob and Alice measure the two photons at angles c and d, they will obtain r, and s" These two statements can both be true at the same time because they both contain their conditioning statements built in. However, this does not mean "x, y, r, and s" must simultaneously exist. Which ones exist, will depend on which of the conditioning statements were actually realized based on which experiment has already been performed. Say Alice and Bob have measure the two photons at angles a and b. At that instance, "x and y" have independent truth values because it is a fact that Alice and Bob have measured at b and a. However, the other statement now becomes a counterfactual statement. "Had Bob and Alice measured the two photons at angles c and d, they would have obtained r, and s". This statement is still true, but "r and s" do not have independent truth values from the conditioning statements. In fact they can never have, because the two photons have already been measured and destroyed in the process.

Bell and his proponents insist that realism must mean "x, y, r and s" all have simultaneous reality independent of any conditioning statements. This is an unreasonable expectation and points to a naive understanding of simple modal logic. You can have a local realistic theory with hidden variables governing photons and still be limited by the fact that Bob and Alice can not repeat their measurement on the same two photons already measured and destroyed. You can even have non-locality with spooky action at a distance and still "x, y, r and s" will not have simultaneous reality for the same simple logical reasons.

Insisting that such a straw-man is the meaning of "realism", effectively renders impossible any experiment that could ever test it, no experimenter can ever recover their photons, restore them to their pristine condition and re-measure them.

 

[billschnieder]

The following highlights the modal error mentioned in my previous post. If you can see the error in the following argument, you will immediately see the logical error being made by Bell proponents:

A photon A is heading toward Alice's detector on a distant galaxy. They will interact tomorrow to produce an outcome of +1 or -1. But the 'laws' of the excluded middle (no third truth-value) and of noncontradiction (not both truth-values), mandate that one of the propositions "Alice's will get +1", "Alice's will get -1", is true (always has been and ever will be) and the other is false (always has been and ever will be). Suppose 'Alice's will get +1' is true today. Then whatever Alice does (or fails to do) before the photon hist her detector will make no difference: the outcome is already settled. Similarly if 'Alice's will get +1' is false today, no matter what Alice does (or fails to do), it will make no difference: the outcome is already settled. Thus, if propositions bear their truth-values timelessly (or unchangingly and eternally), then planning, or as Aristotle put it 'taking care', is illusory in its efficacy. The future will be what it will be, irrespective of our planning, intentions, etc. Free-will is an illusion."

Hint: admit the validity of CFD

 

[JesseM]

Bell and his proponents insist that realism must mean "x, y, r and s" all have simultaneous reality independent of any conditioning statements.

No, they don't. The notion of predetermined values prior to measurements is a deduction that physicists make in scenarios where both experimenters are guaranteed to get identical (or opposite) results whenever they measure the same property, and the deduction also depends on some other assumptions like the assumption of local realism, the no-conspiracy condition, and assumptions about the experimental setup like that the measurements are made at a spacelike separation. But as I pointed out to you in an [post=3275052]earlier post[/post], there are some inequalities like the CHSH inequality that don't depend on the condition that the experimenters always get identical results when they perform the same measurement. I haven't looked at the derivation of the CHSH inequality in a while but I'm fairly certain that here there is no assumption that the measurement results were predetermined prior to measurement, you're free to assume a local realist theory that contains a genuine random element, so that the outcome of any measurement could not have been predicted even with complete knowledge of all hidden and observable variables at some time just prior to measurement.

 

[SpectraCat]

Hidden in the highlighted phrase is a modal fallacy. A prediction MUST always be conditioned on the assumptions, ie it can not be true apart from its conditioning assumptions. For example "If Bob and Alice measure the two photons at angles b and a, they will obtain x, and y" and "If Bob and Alice measure the two photons at angles c and d, they will obtain r, and s" These two statements can both be true at the same time because they both contain their conditioning statements built in. However, this does not mean "x, y, r, and s" must simultaneously exist. Which ones exist, will depend on which of the conditioning statements were actually realized based on which experiment has already been performed. Say Alice and Bob have measure the two photons at angles a and b. At that instance, "x and y" have independent truth values because it is a fact that Alice and Bob have measured at b and a. However, the other statement now becomes a counterfactual statement. "Had Bob and Alice measured the two photons at angles c and d, they would have obtained r, and s". This statement is still true, but "r and s" do not have independent truth values from the conditioning statements. In fact they can never have, because the two photons have already been measured and destroyed in the process.

Bell and his proponents insist that realism must mean "x, y, r and s" all have simultaneous reality independent of any conditioning statements. This is an unreasonable expectation and points to a naive understanding of simple modal logic. You can have a local realistic theory with hidden variables governing photons and still be limited by the fact that Bob and Alice can not repeat their measurement on the same two photons already measured and destroyed. You can even have non-locality with spooky action at a distance and still "x, y, r and s" will not have simultaneous reality for the same simple logical reasons.

Insisting that such a straw-man is the meaning of "realism", effectively renders impossible any experiment that could ever test it, no experimenter can ever recover their photons, restore them to their pristine condition and re-measure them.

That all seems like interpretation to me ... what experimental evidence can you offer that the world actually behaves the way you claim? The experimental evidence shows that coincident measurement statistics for entangled photons violate Bell inequalities (or CHSH inequalities, which I believe are even weaker than Bell inequalities in terms of the assumptions upon which they are based). The experiments do not assume anything a priori about which values will be measured ... can you explain the results in a local realistic fashion?

 

[Rap]

That all seems like interpretation to me ... what experimental evidence can you offer that the world actually behaves the way you claim? The experimental evidence shows that coincident measurement statistics for entangled photons violate Bell inequalities (or CHSH inequalities, which I believe are even weaker than Bell inequalities in terms of the assumptions upon which they are based). The experiments do not assume anything a priori about which values will be measured ... can you explain the results in a local realistic fashion?

If I may answer for billschnieder - The first paragraph is not a description of how the world behaves, it is pure logic, noting that CFD is an additional assumption needed to yield the paradox. The only part where he describes how the world works is to note that it impossible to test for the given description of reality. So, it seems to me, you are asking for experimental evidence that there can be no experimental evidence for the given description of reality.

 

[Rap]

Hidden in the highlighted phrase is a modal fallacy. A prediction MUST always be conditioned on the assumptions, ie it can not be true apart from its conditioning assumptions. For example "If Bob and Alice measure the two photons at angles b and a, they will obtain x, and y" and "If Bob and Alice measure the two photons at angles c and d, they will obtain r, and s" These two statements can both be true at the same time because they both contain their conditioning statements built in. However, this does not mean "x, y, r, and s" must simultaneously exist. Which ones exist, will depend on which of the conditioning statements were actually realized based on which experiment has already been performed. Say Alice and Bob have measure the two photons at angles a and b. At that instance, "x and y" have independent truth values because it is a fact that Alice and Bob have measured at b and a. However, the other statement now becomes a counterfactual statement. "Had Bob and Alice measured the two photons at angles c and d, they would have obtained r, and s". This statement is still true, but "r and s" do not have independent truth values from the conditioning statements. In fact they can never have, because the two photons have already been measured and destroyed in the process.

I agree

 

[JesseM]

If I may answer for billschnieder - The first paragraph is not a description of how the world behaves, it is pure logic, noting that CFD is an additional assumption needed to yield the paradox.

But it's not an assumption, it's derived from the basic assumption of a local realist model, along with the no-conspiracy condition.

 

[Rap]

The following highlights the modal error mentioned in my previous post. If you can see the error in the following argument, you will immediately see the logical error being made by Bell proponents:

A photon A is heading toward Alice's detector on a distant galaxy. They will interact tomorrow to produce an outcome of +1 or -1. But the 'laws' of the excluded middle (no third truth-value) and of noncontradiction (not both truth-values), mandate that one of the propositions "Alice's will get +1", "Alice's will get -1", is true (always has been and ever will be) and the other is false (always has been and ever will be). Suppose 'Alice's will get +1' is true today. Then whatever Alice does (or fails to do) before the photon hist her detector will make no difference: the outcome is already settled. Similarly if 'Alice's will get +1' is false today, no matter what Alice does (or fails to do), it will make no difference: the outcome is already settled. Thus, if propositions bear their truth-values timelessly (or unchangingly and eternally), then planning, or as Aristotle put it 'taking care', is illusory in its efficacy. The future will be what it will be, irrespective of our planning, intentions, etc. Free-will is an illusion."

Hint: admit the validity of CFD

I object to the language - "Then whatever Alice does (or fails to do)" implies she has a choice, while the idea that CFD denies free will contradicts this.

I think "free will" may be a classical concept, with more and more limited applicability as you go to the quantum realm. I say "may be" because I cannot prove it. Thus, I think accepting CFD may be a classical prejudice. When you say "Hint: admit the validity of CFD"... why?

 

[Rap]

But it's not an assumption, it's derived from the basic assumption of a local realist model, along with the no-conspiracy condition.

I think you might be right. I had blinders on, when billschnieder said "If Bob and Alice measure the two photons at angles b and a, they will obtain x, and y" and "If Bob and Alice measure the two photons at angles c and d, they will obtain r, and s". I took that to mean the particular case where a=b and they will obtain x and y=!x (equal and opposite spins), and c=d and they will obtain r and s=!r. This is the only case that is experimentally true, and then the statement is just logic and the acceptance of an experimental truth. His conclusion is still valid, I think.

 

[harrylin]

I said it was sufficient as a definition when I quoted it. I also said that there is no element of reality without that. I meant that per the definition in use. Perhaps you have a better definition.

Strictly speaking, it is certainly possible there is an element of reality WITHOUT us being able to predict it in advance. For example, I had to pay when my son wrecked the car even though I could not predict the amount in advance with certainty. And believe me, that was very real to my pocketbook.

So if you take the contranegative (also being true), you get: IF you cannot predict in advance with certainty, THEN there is no element of reality. But what can you do with this statement? I don't think too much, because you cannot prove the antecedent.

So my point is: Bell used the well accepted EPR definition. That definition is one which is easy to follow, and because it is sufficient it is enough for our examples. I.e. for entangled pairs. The only issue to Bell would be if you could prove convince folks that this was not a sufficient condition. That would be a tough hurdle. Keep in mind that was a cornerstone of EPR.

The issue here is that roughly speaking, Bell tried to prove the inverse of what EPR tried to prove, and that EPR stressed that the inverse of their condition is not true - if I state that an apple is a fruit (so that always apple=>fruit), it does not imply that a fruit is necessarily an apple (NOT fruit=>apple).

However, so far I have not found out if it matters for Bell's Theorem that EPR's condition of predictability is not a necessary condition for reality. I'm just aware that any subtle difference of interpretation about this topic can have great consequences.

I'll be grateful if someone can clarify this to me.

 

[harrylin]

of course you are Right.
Reality is what exist, the state of things as they actually exist. "No Strings Attached".

with CFD or without CFD.

.

You misquoted me: I said if EPR's view was correctly interpreted. However, it appears that they meant with "reality" quite the same as you and me.

 

[harrylin]

A-> B

implies

~B -> ~A

Too bad I reversed it.

OK [edit: I first misread] - using my earlier illustration:

<Apple> => <Fruit> is true;

and

<NOT Fruit> => <NOT Apple> is also true. So we agree now

Harald

 

[JesseM]

The issue here is that roughly speaking, Bell tried to prove the inverse of what EPR tried to prove, and that EPR stressed that the inverse of their condition is not true - if I state that an apple is a fruit (so that always apple=>fruit), it does not imply that a fruit is necessarily an apple (NOT fruit=>apple).

No, Bell did not try to prove the inverse, i.e. he never tried to prove that NOT (values predictable in advance)=>NOT (predetermined values prior to measurement)

 

[billschnieder]

I object to the language - "Then whatever Alice does (or fails to do)" implies she has a choice, while the idea that CFD denies free will contradicts this.

I think "free will" may be a classical concept, with more and more limited applicability as you go to the quantum realm. I say "may be" because I cannot prove it. Thus, I think accepting CFD may be a classical prejudice. When you say "Hint: admit the validity of CFD"... why?

The point is that the argument appears to suggest that everything that will happen in the future is already settled and nothing anyone does or does not do can change it. Do you agree or do you disagree with this and if so why? There is a modal error in such an argument, which I will present in moment after others have had a chance to think about the issue. It will reveal a subtle error being made by Bell proponents over and over.

To give a further hint, consider the following:
a) Statement made on Monday: "Bill will eat do-nuts for breakfast on Tuesday"
b) Statement made on Wednesday: "Bill ate do-nuts for breakfast on Tuesday"
Bill did in fact eat do-nuts for breakfast on Tuesday. So let us rewind time back to Monday, is statement (a) True? Of course both statements are true. Does it mean Bill had no choice or control over what Bill did on Tuesday simply because on Monday it was already true that he will eat do-nuts on Tuesday?

 

[Rap]

The point is that the argument appears to suggest that everything that will happen in the future is already settled and nothing anyone does or does not do can change it. Do you agree or do you disagree with this and if so why? There is a modal error in such an argument, which I will present in moment after others have had a chance to think about the issue. It will reveal a subtle error being made by Bell proponents over and over.

To give a further hint, consider the following:
a) Statement made on Monday: "Bill will eat do-nuts for breakfast on Tuesday"
b) Statement made on Wednesday: "Bill ate do-nuts for breakfast on Tuesday"
Bill did in fact eat do-nuts for breakfast on Tuesday. So let us rewind time back to Monday, is statement (a) True? Of course both statements are true. Does it mean Bill had no choice or control over what Bill did on Tuesday simply because on Monday it was already true that he will eat do-nuts on Tuesday?

I had hoped that I had made it clear that I am not an advocate for rejecting CFD, nor do I advocate against it. I just want to understand the implications of rejecting it, which I do not, at present.

Regarding Bill and the do-nuts. Of course both statements are true, but this is not an illustration of CFD. An illustration would be "If Bill buys do-nuts monday night, he will eat do-nuts for breakfast on Tuesday and if he does not, he will not" According to our model of this phenomenon, this will always happen. We observe a thousand times, Bill buys do-nuts monday night, and every time, he eats do-nuts for breakfast on Tuesday. A thousand times, Bill does not and he does not. Our model has been correct. Now suppose one monday night, Bill does not buy do-nuts, and does not eat do-nuts for breakfast on Tuesday. What is the truth value of the statement "if he had bought do-nuts, he would have eaten do-nuts for breakfast on Tuesday"? This is not the same as saying that if he does, he will. It is saying something definite (he would have eaten do-nuts) about something which is counter-factual (he in fact did not buy do-nuts). On the other hand, to say that if he does, he will, is not counterfactual.

If we reject CFD, then it is improper to even speak about what would have happened. Rejecting CFD, quantum mechanics then only presumes to speak about the future and the factual past, not about a hypothetical past. I don't so much think that rejection of CFD denies free will as it renders the concept improper, not a proper subject for scientific inquiry, an untestable concept, much like the concept of simultaneous position and momentum. And, much like simultaneous position and momentum, in the limit of classical physics, CFD gains meaning. I think that rejecting CFD may be the solution to Bell's paradox, but I don't know. I can't wrap my mind around the concept yet, just like once upon a time I couldn't wrap my mind around not knowing position and momentum simultaneously. Until I learned to identify and reject what amounts to a classical prejudice.

I mean, consider this counter-factual situation: suppose I prepare a system and measure the position of a particle and after many repeated preparations and measurements on many particles, I get the same answer. If, after one of those preparations, I had instead measured the momentum, would the position of the particle at that time been the same as what I have in fact measured in the past? The answer is to reject CFD in this case - the answer to the question is not yes or no, the answer is that the question is improper. If I accept CFD and say yes, it will have the same position, then, knowing the position and momentum will allow me to calculate exactly where it will be measured to be at some time in the future, and when I look for it, chances are it will not be there. A paradox - which may be resolved by rejecting CFD in this case (or assuming hidden variables).

I'm not saying this is a perfect analogy to the Bell paradox, it just ... resonates in my mind.

 

[SpectraCat]

The point is that the argument appears to suggest that everything that will happen in the future is already settled and nothing anyone does or does not do can change it. Do you agree or do you disagree with this and if so why? There is a modal error in such an argument, which I will present in moment after others have had a chance to think about the issue. It will reveal a subtle error being made by Bell proponents over and over.

To give a further hint, consider the following:
a) Statement made on Monday: "Bill will eat do-nuts for breakfast on Tuesday"
b) Statement made on Wednesday: "Bill ate do-nuts for breakfast on Tuesday"
Bill did in fact eat do-nuts for breakfast on Tuesday. So let us rewind time back to Monday, is statement (a) True? Of course both statements are true. Does it mean Bill had no choice or control over what Bill did on Tuesday simply because on Monday it was already true that he will eat do-nuts on Tuesday?

First of all, it seems like statement a) is only "true" if you assume complete determinism of the universe. I don't think everyone is willing to grant that ...

What if I add the following statement on Monday:

a') Courtney will assassinate Bill on Monday evening?

Now it sure seems like only one statement, a or a', can be "true", and we can't know which one until after the events have passed. Therefore it seems that one cannot make judgments about the truth of a (or a') until the event has already occurred. In a deterministic universe, I suppose one of the statements could be said to have been "true all along" ... but you cannot know that until after the fact, so it just seems like interprative post-rationalization to me. There is no way to use such scenarios to empirically deduce whether or not the universe is deterministic.

 

[Rap]

Now it sure seems like only one statement, a or a', can be "true", and we can't know which one until after the events have passed. Therefore it seems that one cannot make judgments about the truth of a (or a') until the event has already occurred. In a deterministic universe, I suppose one of the statements could be said to have been "true all along" ... but you cannot know that until after the fact, so it just seems like interprative post-rationalization to me. There is no way to use such scenarios to empirically deduce whether or not the universe is deterministic.

I'm taking the statement "Bill will eat do-nuts on Tuesday for breakfast" in the same sense that if Alice and Bob align their detectors and make measurements, "Alice and Bob will measure equal and opposite spins".

 

[SpectraCat]

I'm taking the statement "Bill will eat do-nuts on Tuesday for breakfast" in the same sense that if Alice and Bob align their detectors and make measurements, "Alice and Bob will measure equal and opposite spins".

But it's not the same. The corresponding statement about Bill that could (perhaps) be correlated the the Alic and Bob example is, if Bill is alive on Tuesday, and if he is awake in the morning, and if he is hungry, and if donuts are the only available food, (there are lots more qualifiers needed, but I guess you get the idea) then Bill will eat donuts for breakfast on Tuesday.

The Alice & Bob statement is based on a theory of physics that has been extensively tested and has never been found to be false. Making that statement is equivalent to saying, "Quantum mechanics is expected to still be valid when Alice and Bob make their measurements".