Scholarpedia article on Bell's Theorem

[Nugatory]

One happy outcome of this thread

It provoked me to buy the second edition of "Speakable and Unspeakable", just for the "Nouvelle Cuisine" essay. This was money well-spent.

 

[DevilsAvocado]

Let me summarize my own viewpoint, and let's see how much agreement I can get. Let's suppose that QM is correct about all its experimental predictions. Then whenever you turn the polarizers to the same angle, you will get perfect correlation. From this you can reach three possible conclusions:

1. Even when you don't turn the polarizers to the same angle, it is still true that if you HAD turned the polarizers to the same angle, you WOULD have gotten perfect correlation.
2. When you don't turn the polarizes to the same angle, it makes no sense to ask what would have happened if you had turned them to the same angle.
3. When you don't turn the polarizers to the same angle, then it may be the case that you wouldn't have gotten perfect correlation if you had turned them to the same angle.

If we assume the principle of locality (i.e. excluding backward causation), then the only way option 3 would be possible is if the photons "knew" in advance what angle the polarizers would be turned to, or equivalently whatever is controlling the experiment decisions about the polarizer settings "knew" in advance whether the two photons would do the same thing or not. That would be superdeterminism, and we exclude it by the no-conspiracy condition.

So now we have two options left. Quantum mechanics takes option 2. But if you believe in counterfactual definiteness, you are forced into option 1. And then if you accept option 1 and the principle of locality (again, excluding backward causation), you are forced to conclude that the decision of each photon to go through or not go through must be determined by local hidden variables that are shared by the two photons. Is this a fair summary of the EPR argument?

I don’t know what to say about paragraph 3, it seems to require some ‘inconsistent law of nature’... that I have never heard of...

Paragraph 2 seems to be correct (if you live in Copenhagen ;).

Paragraph 1 is a little bit trickier, because I don’t think that counterfactual definiteness is the premise here. As I get counterfactual definiteness, it’s about two non-commuting quantities that cannot have simultaneous “reality” (i.e. real values). AFAIK, there’s nothing counterfactual about both A & B being measured "up" at 0°, is it?

What about the EPR argument? Well, today we know that both Einstein & Bohr was wrong to some extent, so does it really matter for current discussion? And furthermore, the EPR paper was written by Podolsky (and some say published without Einstein's confirmation).

So, what did Einstein really think about counterfactual definiteness? Well, it’s clearly not the same sausage that Podolsky was chewing on:

http://plato.stanford.edu/entries/qt-epr/]...[/PLAIN] as early as June 19, 1935 Einstein makes it plain that he is not especially interested in the question of simultaneous values for incompatible quantities like position and momentum. Just as in Solvay 1927, the concern that he expresses to Schrödinger is with the question of completeness, given the resources of the quantum theory, in describing the situation concerning a single variable (maybe position, maybe momentum). With respect to the treatment of an incompatible pair he tells Schrödinger “ist mir wurst”—literally, it's sausage to me; i.e., he couldn't care less. (Fine 1996, p. 38). In his writings subsequent to EPR, Einstein probes an incompatibility between affirming locality and separability, on the one hand, and completeness in the description of individual systems by means of state functions, on the other. His argument is that we can have at most one of these but never both. He frequently refers to this dilemma as a “paradox”.

[my bolding]

Don’t ask me if it’s fair or not, it’s just the way it is (I think).

 

[lugita15]

I don’t know what to say about paragraph 3, it seems to require some ‘inconsistent law of nature’... that I have never heard of...

(Are we allowed to post in a year-old thread?) There's no inconsistency in option 3, AKA superdeterminism. Option 3 is basically that the photons "know" in advance what choice of measurement you're going to make, so they back at the source they "agree" upon what they'll do in response. So the only reason the polarizers give the same results when you turn both polarizers to the same angle is that the photons know you're going to turn both polarizers to the same angle.

But, on those occasions when you DON'T turn both polarizers to the same angle, it's no longer true that the polarizer would have given the same results if you DID turn them to the same angle. To put it another way, according to superdeterminism the two photons agree on what they're going to do based on what they think you're going to do. But if, after the photons have made the decision on what they're going to do, you somehow swallowed a magic "free will pill" that allow you to make a different measurement decision than the one they were anticipating, then you would find that the polarizers do not give the same results if your turn them to the same angle.

Does that make more sense?

Paragraph 2 seems to be correct (if you live in Copenhagen ;).

Yes, option 2 is what the Copenhagen interpretation adopts. It rejects as meaningless counterfactual statements, i.e. it rejects counterfactual definiteness.

Paragraph 1 is a little bit trickier, because I don’t think that counterfactual definiteness is the premise here. As I get counterfactual definiteness, it’s about two non-commuting quantities that cannot have simultaneous “reality” (i.e. real values). AFAIK, there’s nothing counterfactual about both A & B being measured "up" at 0°, is it?

There is something counterfactual, when you don't both polarizers to 0 degrees, but then you ask what results you would get if you had set them to 0 degrees. So you're talking about what result a 0 degree polarization measurement would yield, even though the measurement you actually made was of an observable which is non-commuting with the 0 degree polarization observable. So how is that not assuming counterfactual definiteness?

What about the EPR argument? Well, today we know that both Einstein & Bohr was wrong to some extent, so does it really matter for current discussion? And furthermore, the EPR paper was written by Podolsky (and some say published without Einstein's confirmation).

So, what did Einstein really think about counterfactual definiteness? Well, it’s clearly not the same sausage that Podolsky was chewing on:

Well, it doesn't matter what Albert Einstein thought, it matters whether EPR is a valid argument. And in my mind, it seems like the EPR argument is valid: it showed (assuming no superdeterminism, AKA the no-conspiracy condition) that locality + counterfactual definiteness implies that it is determined in advance what polarizer angles the photons will go through, and what polarizer angles the photons will not go through.

ttn, on the other hand, thinks that locality on its own, along with the no-conspiracy condition, implies the "determined in advance" thing, and that you don't need the counterfactual definiteness at all. I disagree, because I think you can't even state the no-conspiracy condition without talking about counterfactuals. (See my discussion of option 3 above.)

 

[zhanhai]

"Bell's theorem states that the predictions of quantum theory (for measurements of spin on particles prepared in the singlet state) cannot be accounted for by any local theory. "

I would think that "any local theory" should be "any classical local theory" .

 

[Doc Al]

"Bell's theorem states that the predictions of quantum theory (for measurements of spin on particles prepared in the singlet state) cannot be accounted for by any local theory. "

I would think that "any local theory" should be "any classical local theory" .

Meaning what, exactly?

 

[DevilsAvocado]

(Are we allowed to post in a year-old thread?)

Why not? After all, Niels & Albert was quibbling about this stuff for almost 30 years...

[and Doc Al is here = it’s cool]

There's no inconsistency in option 3, AKA superdeterminism. Option 3 is basically that the photons "know" in advance what choice of measurement you're going to make, so they back at the source they "agree" upon what they'll do in response. So the only reason the polarizers give the same results when you turn both polarizers to the same angle is that the photons know you're going to turn both polarizers to the same angle.

Okay, superdeterminism. Again my picture is slightly different, in superdeterminism everything is predetermined; from your thoughts on the experiment, to the final settings of the rotating polarizers, and the state of the entangled photons = totally ridicules because this makes the universe a hoax that trick us to believe there are “laws” out there to discover, when all that exist in this case is just a “badly written story”.

To put it another way, according to superdeterminism the two photons agree on what they're going to do based on what they think you're going to do.

In superdeterminism any choice is illusionary; everything is permanently set and written in stone from t₀.

Yes, option 2 is what the Copenhagen interpretation adopts. It rejects as meaningless counterfactual statements, i.e. it rejects counterfactual definiteness.

Yep, and Bohr also rejected any ‘meaningfulness’ to the QM world:

There is no quantum world. There is only an abstract physical description. It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature...

Hence, it does not make any sense to talk about counterfactual definiteness, since when we carry out the measurement – it’s gone.

There is something counterfactual, when you don't both polarizers to 0 degrees, but then you ask what results you would get if you had set them to 0 degrees. So you're talking about what result a 0 degree polarization measurement would yield, even though the measurement you actually made was of an observable which is non-commuting with the 0 degree polarization observable. So how is that not assuming counterfactual definiteness?

I’m not an expert on counterfactual definiteness (and I’m chewing on the same sausage as Einstein ;) but to me it looks like you include the entire universe in the ‘counterfactual state’, right? You hypothesize “what would have happened if I did that instead of this”, right? And you could make statements like “I did not play on the lottery, but if I had, I could be a millionaire”, right?

This is not my picture. Counterfactual definiteness to me means simultaneous values for incompatible quantities in a single object/particle, not the state of entire universe. And I think the reason for EPR to include counterfactual definiteness was to show that these incompatible quantities (not possible to measure according to QM) was after all there and they were real, and the only reason we couldn’t measure them directly was due to human imperfection, not nature.

Well, it doesn't matter what Albert Einstein thought,

Really!? Einstein was the ‘Commander-in-Chief’ in the ‘QM-war’!

it matters whether EPR is a valid argument. And in my mind, it seems like the EPR argument is valid:

Well, if you exclude Einstein all you get is a simple "PR argument"... Seriously, today there is absolutely no doubt that the EPR argument is invalid.

it showed (assuming no superdeterminism, AKA the no-conspiracy condition) that locality + counterfactual definiteness implies that it is determined in advance what polarizer angles the photons will go through, and what polarizer angles the photons will not go through.

Nah... EPR tried to show that there is an existing Local Reality (still unknown, but it must be there). Because Einstein thought it to be totally ridicules to have particles acting on each other “at a spooky distance” (and it was also a serious threat to SR), that he took it for granted that these entangled values had to be there, existing from the beginning. But this assumption was obviously wrong.

We must remember that Einstein & Bohr only discussed perfect correlations and thus could never settle on the right answer (because perfect correlations are impossible to separate from “tossing coins/gloves in a box” -type of correlations).

ttn, on the other hand, thinks that locality on its own, along with the no-conspiracy condition, implies the "determined in advance" thing, and that you don't need the counterfactual definiteness at all. I disagree, because I think you can't even state the no-conspiracy condition without talking about counterfactuals. (See my discussion of option 3 above.)

AFAIK, these are the contemporary options:

• Locality
• Realism
• Free will

Bell’s theorem stipulates that QM violates at least one of these three assumptions.

From this it’s easy to see that the only way to have Locality + predetermined values (i.e. Realism) – is to sacrifice Free will (this is the only option that I see compatible to “EPR counterfactual definiteness”).

Or, you could have non-locality + predetermined values (i.e. Realism) – this would be the de Broglie-Bohm theory (i.e. “EPR incompatible”).

Or, you could have Locality + undetermined values (i.e. non-realism/non-separability) – this would be some kind of a non-separable blockworld/holism (i.e. “very EPR incompatible”). Freaky stuff under development...

Or, you could have non-locality + non-separability – this would be real scary stuff!

Remember it’s a no-go theorem...

 

[Ilja]

I would definitely say that the vast majority of published articles dismiss the idea that particle observables have well-defined values at all times. You may consider that an imprecise definition of realism, but nonetheless I would say it is the most common.

Common may be possible - unfortunately. Because it does not make sense at all. Of course, the results of some interaction wrongly described as an "observation" will not be predefined by the state of the "observed object" already in common sense realism. So, any "solution" of the violation of Bell's inequality which is based on such a rejection simply repeats the most common error of understanding Bell's theorem - that there is a predefined value A(a,l) for every angle a is not assumed but derived using the EPR argument and, therefore, Einstein causality.

 

[Ilja]

Okay, superdeterminism. Again my picture is slightly different, in superdeterminism everything is predetermined; from your thoughts on the experiment, to the final settings of the rotating polarizers, and the state of the entangled photons = totally ridicules because this makes the universe a hoax that trick us to believe there are “laws” out there to discover, when all that exist in this case is just a “badly written story”.

Indeed, superdeterminism is quite stupid. But nonetheless, I prefer another argument against superdeterminism: It doesn't save Einstein causality. Because with superdeterminism even a working FTL phone line to Andromeda would be unable to prove that Einstein causality is wrong. So, Einstein causality becomes unfalsifiable by observation.

Nah... EPR tried to show that there is an existing Local Reality (still unknown, but it must be there).

Not exactly. The EPR argument assumes Einstein causality, it does not even try to derive it. And starting from this assumption, it follows that the 100% correlation requires a common cause in the past which predefines the outcome. This is a valid argument.

From this it’s easy to see that the only way to have Locality + predetermined values (i.e. Realism) – is to sacrifice Free will (this is the only option that I see compatible to “EPR counterfactual definiteness”).

It does not help. Without free will, Einstein causality (unfortunately named locality) becomes unfalsifiable and therefore worthless from a scientific point of view.

And, second, I see here the most common error in understanding Bell's theorem again: The predetermied values are not at all the same as realism. The predetermined values are not assumed in Bell's theorem, they are derived in the first step, using the EPR argument, and, therefore, Einstein causality.

No free will would be - if taken seriously and applied everywhere - the end of science.
No realism would be - if taken seriously and applied everywhere - the end of science.

No Einstein causality would be, instead, harmless. Science has been quite successful in the Newtonian time, but Newtonian theory was also "nonlocal".

 

[lugita15]

Okay, superdeterminism. Again my picture is slightly different, in superdeterminism everything is predetermined; from your thoughts on the experiment, to the final settings of the rotating polarizers, and the state of the entangled photons = totally ridicules because this makes the universe a hoax that trick us to believe there are “laws” out there to discover, when all that exist in this case is just a “badly written story”.

(Sorry it took me so long to respond.)

OK, let's be careful here. I think the rejection of free will is not enough on its own to escape Bell's theorem; even if the experimenter doesn't have control over his measurement decisions, it may still be the case that the actions of the photons are not based on what the experimenter will do, so Bell's inequality would still have to hold. So what is required to escape Bell's theorem is for the actions of the photons to be just right to account for the measurement decisions the experimenter is going to make.

And so the no-conspiracy condition needs to eliminate this possibility: it needs to say that the question "What would this photon do if it were confronted with a polarizer oriented at this angle?" is independent of what angles the experimenter is going to set the two polarizers to.

In superdeterminism any choice is illusionary; everything is permanently set and written in stone from t₀.

It's certainly true that there's no free will in superdeterminism, but that's equally true of determinism in general. It's also true of determinism in general that the future course of the universe is entirely determined given the initial state of the universe.

You seem to think that the "super" part of superdeterminism is that the future course of the universe is fixed by fiat, as opposed to being determined by deterministic laws. But I don't think it matters for the purposes of Bell's theorem whether deterministic laws or fiat determines the measurement decisions of the experimenter. As I said, all that is required to evade the conditions needed for Bell's theorem to hold is that the experimenter cannot freely choose his measurement decisions, AND the behavior of the photons is such that it violates the Bell inequality, given what the experimenter is going to do.

I’m not an expert on counterfactual definiteness (and I’m chewing on the same sausage as Einstein ;) but to me it looks like you include the entire universe in the ‘counterfactual state’, right? You hypothesize “what would have happened if I did that instead of this”, right? And you could make statements like “I did not play on the lottery, but if I had, I could be a millionaire”, right?

Well, I suppose that taken literally, "counterfactual definiteness" means the meaningfulness of any counterfactual statements, so any statements of the form "If A had been true, B would be true." So yes, the literal meaning of the phrase would encompass how the state of the entire universe would be affected if you had done something. But we don't need all that for the purposes of Bell's theorem.


All we need is the meaningfulness of statements of the form "If we had measured this observable, this is the value that we would have gotten." So I don't think we're really that far apart in our understanding of counterfactual definiteness in the context of Bell's theorem. To me, all it says is that if you measure one observable, say position, then it's still meaningful to ask, and there's a definite answer to, the question "What value would we have gotten if we had instead measured momentum?"

This is not my picture. Counterfactual definiteness to me means simultaneous values for incompatible quantities in a single object/particle, not the state of entire universe.

I'm not talking about the state of entire universe either. I'm just talking about the values that unmeasured observables would have yielded had they been measured.

And I think the reason for EPR to include counterfactual definiteness was to show that these incompatible quantities (not possible to measure according to QM) was after all there and they were real, and the only reason we couldn’t measure them directly was due to human imperfection, not nature.

I think we're in complete agreement on that point.

Seriously, today there is absolutely no doubt that the EPR argument is invalid.

Are you sure you meant to say invalid? Do you mean unsound? An argument is valid if its premises imply its conclusion, independent of whether its premises are true or not. An argument is sound if it is valid and its premises are true.

To my mind, the EPR argument is that, perfect correlations at identical angles + locality + counterfactual definiteness implies local hidden variables. And that argument seems perfectly valid to me, at least if we throw in the no-conspiracy condition.

Nah... EPR tried to show that there is an existing Local Reality (still unknown, but it must be there). Because Einstein thought it to be totally ridicules to have particles acting on each other “at a spooky distance” (and it was also a serious threat to SR), that he took it for granted that these entangled values had to be there, existing from the beginning.

Yes, I think we're agreed on that.

But this assumption was obviously wrong.

Well, either locality or one of the other assumptions is wrong.

We must remember that Einstein & Bohr only discussed perfect correlations and thus could never settle on the right answer (because perfect correlations are impossible to separate from “tossing coins/gloves in a box” -type of correlations).

I agree with that.

AFAIK, these are the contemporary options:

• Locality
• Realism
• Free will

Bell’s theorem stipulates that QM violates at least one of these three assumptions.

From this it’s easy to see that the only way to have Locality + predetermined values (i.e. Realism) – is to sacrifice Free will (this is the only option that I see compatible to “EPR counterfactual definiteness”).

Like I said above, rejecting free will is not enough to escape Bell. So if QM violates locality and realism (AKA counterfactual definiteness), then it violates free will and more: it violates the principle that the value that a measurement would yield if you perform doesn't depend on whether you're actually going to perform it or not.

Finally, can you weigh in on the argument ttn and I have been having? ttn thinks that locality + no-conspiracy condition implies local hidden variables, but I think that only locality + counterfactual definiteness + no-conspiracy condition is enough to imply local hidden variables.

 

[DevilsAvocado]

OK, let's be careful here. I think the rejection of free will is not enough on its own to escape Bell's theorem; even if the experimenter doesn't have control over his measurement decisions, it may still be the case that the actions of the photons are not based on what the experimenter will do, so Bell's inequality would still have to hold. So what is required to escape Bell's theorem is for the actions of the photons to be just right to account for the measurement decisions the experimenter is going to make.

And so the no-conspiracy condition needs to eliminate this possibility: it needs to say that the question "What would this photon do if it were confronted with a polarizer oriented at this angle?" is independent of what angles the experimenter is going to set the two polarizers to.

It's certainly true that there's no free will in superdeterminism, but that's equally true of determinism in general. It's also true of determinism in general that the future course of the universe is entirely determined given the initial state of the universe.

You seem to think that the "super" part of superdeterminism is that the future course of the universe is fixed by fiat, as opposed to being determined by deterministic laws. But I don't think it matters for the purposes of Bell's theorem whether deterministic laws or fiat determines the measurement decisions of the experimenter. As I said, all that is required to evade the conditions needed for Bell's theorem to hold is that the experimenter cannot freely choose his measurement decisions, AND the behavior of the photons is such that it violates the Bell inequality, given what the experimenter is going to do.

... Maybe I was wooly, but that is exactly what I meant; determinism + no free will = superdeterminism.

I haven’t spent much time thinking on hard/super -determinism, not much to speculate on in this (utterly boring ) world picture:

There is a way to escape the inference of superluminal speeds and spooky action at a distance. But it involves absolute determinism in the universe, the complete absence of free will. Suppose the world is super-deterministic, with not just inanimate nature running on behind-the-scenes clockwork, but with our behavior, including our belief that we are free to choose to do one experiment rather than another, absolutely predetermined, including the "decision" by the experimenter to carry out one set of measurements rather than another, the difficulty disappears. There is no need for a faster than light signal to tell particle A what measurement has been carried out on particle B, because the universe, including particle A, already "knows" what that measurement, and its outcome, will be.

To me, all it says is that if you measure one observable, say position, then it's still meaningful to ask, and there's a definite answer to, the question "What value would we have gotten if we had instead measured momentum?"

Okay, we have more or less the same view on this one. However, there is one little caveat that I think maybe could fool us a little bit when it comes to CFD. If we take momentum and position for example, all this ‘commotion’ is due to fact that we (almost automatically) think of electrons and photons etc as particles. But how do we calculate the properties of the particle? With the Schrödinger wave equation of course, which leads to next question: Does the wavefunction possesses inherent inconsistencies when it comes to ‘translate’ the outcome to a localized particle with a definite momentum and position??

The answer is YES!

Why!? Well, the logic is very simple: Assume we want to measure the exact frequency of a ‘normal’ sound wave – at an exact location in space. Can we do this? Nope, it’s impossible! To get the exact frequency you have to measure the sound wave for some time (at least one cycle), and there goes your exact location down the drain.

My personal guess is that Einstein (of course) had thought of this, and this is the reason he wrote to Schrödinger “ist mir wurst” (i.e. it's sausage to me).

That’s why I’m skeptic to put too much focus on CFD, since it seems pointing towards the Measurement Problem, rather than the question of an independent reality...

Are you sure you meant to say invalid? Do you mean unsound? An argument is valid if its premises imply its conclusion, independent of whether its premises are true or not. An argument is sound if it is valid and its premises are true.

To my mind, the EPR argument is that, perfect correlations at identical angles + locality + counterfactual definiteness implies local hidden variables. And that argument seems perfectly valid to me, at least if we throw in the no-conspiracy condition.

Well... maybe that was clumsy, however the title of the 1935 EPR paper was “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?” and today we know that the rock hard EPR assumption of Local Realism is indeed very incomplete, and most agree it’s now empirically proven wrong. A complete overturn that I’m pretty sure Einstein never expected (but there’s no doubt to me that he, if alive today, would accept the experimental results).

Like I said above, rejecting free will is not enough to escape Bell.

Then you’re on collision with John Bell.

So if QM violates locality and realism (AKA counterfactual definiteness), then it violates free will and more: it violates the principle that the value that a measurement would yield if you perform doesn't depend on whether you're actually going to perform it or not.

I’m not sure I understand “QM violates locality and realism”... it’s perfectly sufficient with locality or realism... and free will is preserved if you give up locality for example...

Finally, can you weigh in on the argument ttn and I have been having? ttn thinks that locality + no-conspiracy condition implies local hidden variables, but I think that only locality + counterfactual definiteness + no-conspiracy condition is enough to imply local hidden variables.

Well, Travis is a dBB guy and I never understand what they’re talking about...

Locality + Free will (no-conspiracy) = Realism (LHV)??

That doesn’t work, does it??

Locality + Realism (CFD) + Free will (no-conspiracy) = Realism (LHV)?

I’m completely lost here...

 

[lugita15]

As I said, all that is required to evade the conditions needed for Bell's theorem to hold is that the experimenter cannot freely choose his measurement decisions, AND the behavior of the photons is such that it violates the Bell inequality, given what the experimenter is going to do.

... Maybe I was wooly, but that is exactly what I meant; determinism + no free will = superdeterminism.

Hmm, but what I said in bold is different from determinism + no free will = superdeterminism. (Although I do agree that superdeterminism implies determinism + no free will.) I think determinism + no free will is not enough on its own to escape Bell's theorem, because the behavior of the photons may be completely independent of what the experimenter will do. That's why the part after the "AND" is necessary in the bolded statement: what the photon "agree" to do beforehand has to depend (in just the right way) on what they "know" the experimenter will do later.

I haven’t spent much time thinking on hard/super -determinism, not much to speculate on in this (utterly boring ) world picture:
"There is a way to escape the inference of superluminal speeds and spooky action at a distance. But it involves absolute determinism in the universe, the complete absence of free will. Suppose the world is super-deterministic, with not just inanimate nature running on behind-the-scenes clockwork, but with our behavior, including our belief that we are free to choose to do one experiment rather than another, absolutely predetermined, including the "decision" by the experimenter to carry out one set of measurements rather than another, the difficulty disappears. There is no need for a faster than light signal to tell particle A what measurement has been carried out on particle B, because the universe, including particle A, already "knows" what that measurement, and its outcome, will be."

The quote from the BBC interview may be cut off, because after that he says something to the effect of "Even if you made measurement decisions using deterministic random number generators, the decisions may be effectively free for our purposes, since it's determined by a large number of tiny effects." In other words, even if the universe is deterministic and there's no free will, the no-conspiracy condition may still hold, because what the photons "plan" to do may not be dependent on whatever is controlling the measurement decisions, like the inputs to a random number generator.

Okay, we have more or less the same view on this one. However, there is one little caveat that I think maybe could fool us a little bit when it comes to CFD. If we take momentum and position for example, all this ‘commotion’ is due to fact that we (almost automatically) think of electrons and photons etc as particles.

Well, the beauty of Bell's theorem is that it doesn't depend on what the underlying objects are. As discussed in the other thread, Bell said "the following argument will not mention particles, nor indeed fields, nor any particular picture of what goes on at the microscopic level." We don't need to even think of observables like position, momentum and spin as attributes of objects. We can just talk about the results that measuring devices give, and we can word all our assumptions and conclusions instead of that. So counterfactual definiteness just becomes an issue of whether, if you actually did one thing to a device, it is meaningful to talk about what the device would do if you instead had done something else to it.

Well... maybe that was clumsy, however the title of the 1935 EPR paper was “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?” and today we know that the rock hard EPR assumption of Local Realism is indeed very incomplete, and most agree it’s now empirically proven wrong. A complete overturn that I’m pretty sure Einstein never expected (but there’s no doubt to me that he, if alive today, would accept the experimental results).

Yes, we have pretty firm evidence against the conclusion of the EPR argument, namely local hidden variables, so we have pretty firm grounds for rejecting at least one of the assumptions. But the argument is still logically valid.

Then you’re on collision with John Bell.

I don't think so, as I discussed above.

I’m not sure I understand “QM violates locality and realism”... it’s perfectly sufficient with locality or realism... and free will is preserved if you give up locality for example...

Sorry, I made a mistake in that sentence. I meant to say "So if QM violates NEITHER locality NOR realism (AKA counterfactual definiteness), then it violates free will and more: it violates the principle that the value that a measurement would yield if you perform doesn't depend on whether you're actually going to perform it or not."

Well, Travis is a dBB guy and I never understand what they’re talking about...

Locality + Free will (no-conspiracy) = Realism (LHV)??

That doesn’t work, does it??

Well, at least I don't think it works, but you can see his argument for it here. (It's the paragraph that starts with "Here is the formulation of the "several axes" version of the EPR argument that does not involve counterfactuals.") It basically boils down to the following: rejecting counterfactual definiteness amounts to saying that the question of what elements of reality exist beforehand depends on measurement decisions afterwards, and this would lead to a violation of the no-conspiracy conditiion.

But I think you can't even state the no-conspiracy condition without using counterfactual statements, so without counterfactual definiteness the no-conspiracy condition is meaningless.

Locality + Realism (CFD) + Free will (no-conspiracy) = Realism (LHV)?

I’m completely lost here...

Well, this is exactly what I think a fair summary of the heart of the EPR argument: if the universe obeys locality and counterfactual definiteness, then there must exist local hidden variables (i.e. elements of reality) to supplement quantum mechanics. (EPR didn't mention the no-conspiracy condition, but I think they just took it for granted.)

 

[DevilsAvocado]

I think determinism + no free will is not enough on its own to escape Bell's theorem, because the behavior of the photons may be completely independent of what the experimenter will do.
[...]
In other words, even if the universe is deterministic and there's no free will, the no-conspiracy condition may still hold, because what the photons "plan" to do may not be dependent on whatever is controlling the measurement decisions, like the inputs to a random number generator.

And there are others who have a different view on free will and determinism:

[...] if you assume a completely determined world where everything that happened, absolutely everything, were fixed in a vast network of cause and effect. Then sometime in the past there would be an event that determined both my choice of the measuring instrument and the particle's behavior. Then my choice would no longer be a choice, the random accident would be no accident and the action at a distance would not be action at a distance.

[my emphasis]

Personally I put superdeterminism on the same shelf as all the other loophole madness. It’s a waste of time:

We always implicitly assume the freedom of the experimentalist... This fundamental assumption is essential to doing science. If this were not true, then, I suggest, it would make no sense at all to ask nature questions in an experiment, since then nature could determine what our questions are, and that could guide our questions such that we arrive at a false picture of nature.

Funny anecdote; when Zeilinger was younger he intentionally insulted an advocate of complete determinism, publicly at a conference, which made him quite incensed. Then Zeilinger said to him:

"Why are you getting so upset? Neither you nor I are free in what we do."

Touché!

Well, the beauty of Bell's theorem is that it doesn't depend on what the underlying objects are. [...] So counterfactual definiteness just becomes an issue of whether, if you actually did one thing to a device, it is meaningful to talk about what the device would do if you instead had done something else to it.

I wasn’t talking about Bell's theorem, but how much ‘power’ one should put on CFD in relation to Realism... I think both stands on their own, with or without Bell...

Well, at least I don't think it works, but you can see his argument for it here. (It's the paragraph that starts with "Here is the formulation of the "several axes" version of the EPR argument that does not involve counterfactuals.") It basically boils down to the following: rejecting counterfactual definiteness amounts to saying that the question of what elements of reality exist beforehand depends on measurement decisions afterwards, and this would lead to a violation of the no-conspiracy conditiion.

But I think you can't even state the no-conspiracy condition without using counterfactual statements, so without counterfactual definiteness the no-conspiracy condition is meaningless.

Okay, this is about the EPR argument:

The second observation is that also the more general "several axes" version of the EPR argument — establishing the existence of pre-determined outcomes for measurements of spin along several axes at once — can be formulated without any counterfactuals and is therefore also immune to the alleged rebuttal discussed above. (Of course, it is this "several axes" version of the EPR argument which is needed for Bell's theorem.)

Here is the formulation of the "several axes" version of the EPR argument that does not involve counterfactuals: in order to explain (without violation of locality) the fact that the outcomes will be perfectly anti-correlated if the experimenters both measure spin along the z-axis, one has to assume that these outcomes are pre-determined. The same goes for measurements of spin along the x-axis. Even though, in each run of the experiment, either the z-axis or the x-axis is chosen along which to perform the measurements, the elements of physical reality that exist before the measurements cannot depend on choices that will be made later by the experimenters! This, indeed, doesn't follow from the assumption of locality itself but it does follow from the so-called "no conspiracy" assumption which states, roughly speaking, that the pair of particles prepared by the source does not "know" in advance what experiments are going to be performed on them later.

[my emphasis]

The reasoning is correct; however to me kind of ridicules... any “homemade expert” (like me) can construct a LHV that would make it through this “test”... I simply construct a LHV that randomly set my particles to Az = not(Bz) and Ax = not(Bx), I don’t get this at all... no conspiracy as far as I can see...

This has nothing to do with “creating reality afterwards”, it just a ridicules way of getting rid of all CFD problems...

Locality + Realism (CFD) + Free will (no-conspiracy) = Realism (LHV)?

Well, this is exactly what I think a fair summary of the heart of the EPR argument: if the universe obeys locality and counterfactual definiteness, then there must exist local hidden variables (i.e. elements of reality) to supplement quantum mechanics. (EPR didn't mention the no-conspiracy condition, but I think they just took it for granted.)

But... this ‘equation’ doesn’t work... you have Realism on both left and right-hand side, with additional ‘values’ on left-hand...

This is how I get the original 1935 EPR argument:

Locality + Realism (LHV/CFD) ≠ QM

And Einstein took locality for granted, and the new entanglement feature gave good hope of proving CFD as a fact, which would lead to LHV and Realism... but it goofed, and today’s 180° overturn is a fact:

QM = True
QM ≠ Locality + Realism (LHV/CFD)

 

[billschnieder]

Unanswered Challenge

Earlier in this thread, I posted the following challenge and it remains unanswered for more than a year:

NOTE, the following is simply a mathematics exercise, no physics whatever, but it clearly shows the problem Bell proponents are still unable to see:

Consider the CHSH inequality:

|E(a)E(b) - E(a)E(c)| + |E(d)E(b) + E(d)E(c)| ≤ 2, where E(a), E(b), E(c), E(d) ∈ [−1,1]

This inequality is violated IFF

(1) |E(a)E(b) - E(a)E(c)| + |E(d)E(b) + E(d)E(c)| > 2

We are interested to understand the mathematical properties of the 4 terms E(a), E(b), E(c), E(d) when this violation happens

From (1) we have via factorization

(2) |E(a)||E(b) - E(c)| + |E(d)||E(b) + E(c)| > 2

However, since E(a), E(b), E(c), E(d) ∈ [−1,1], it follows that
|E(b) - E(c)| ≤ 2 and |E(b) + E(c)| ≤ 2

Let us consider the different possible extremes of the values for E(b) and E(c).

If E(b) = E(c) then |E(a)||E(b) - E(c)| = 0 and |E(d)||E(b) + E(c)| must be greater than 2 for equation (1) to hold. But we know that |E(b) + E(c)| ≤ 2 which means |E(d)| must be greater than 2 which is impossible given that E(d) ∈ [−1,1].

If E(b) = -E(c) then |E(a)||E(b) + E(c)| = 0 and |E(a)||E(b) - E(c)| must be greater than 2 for equation (1) to hold. But we know that |E(b) - E(c)| ≤ 2 which means |E(a)| must be greater than 2 which is impossible given that E(a) ∈ [−1,1].

Therefore (1) is mathematically impossible. It is not possible mathematically to violate the CHSH inequality even before we start talking about any physics and what the terms might mean in any physical situation. This is the simple fact that Bell proponents are blind to.

I challenge anyone to find values for E(a), E(b), E(c), E(d) ∈ [−1,1] that violate the above inequality from any source whatsoever using any means whatsoever (local or non-local). You can even assume that E(a) are averages over many runs or whatever you like.

 

[DevilsAvocado]

I challenge anyone to find values for E(a), E(b), E(c), E(d) ∈ [−1,1] that violate the above inequality from any source whatsoever using any means whatsoever (local or non-local). You can even assume that E(a) are averages over many runs or whatever you like.

Elementary my dear Watson, let’s use the Bell parameter of the CHSH inequality:
S = E(a, b) - E(a, b') + E(a', b) + E(a' b')

The "Bell test angles":
a = 0°
a' = 45°
b = 22.5°
b' = 67.5°

Gives:
S = E(0°, 22.5°) - E(0°, 67.5°) + E(45°, 22.5°) + E(45°, 67.5°)

And the relative angles (a-b) are:
S = E(22.5°) - E(67.5°) + E(22.5°) + E(22.5°)

Then calculate for good old Malus classical polarizer cos^2(θ):
S = E(0.85) - E(0.14) + E(0.85) + E(0.85)

And sum up:
S = 2.41

Voila monsieur!

 

[lugita15]

And there are others who have a different view on free will and determinism:

I think this may just be a semantic issue. I would be in complete agreement with Zeilinger's quote if it was modified to "Then my choice would no longer be a choice, the random accident MIGHT be no accident and the action at a distance MIGHT not be action at a distance." The only point I was making was that complete determinism and the lack of free will are necessary but not sufficient conditions to evade Bell's theorem, because the photons may not do the right things.

I wasn’t talking about Bell's theorem, but how much ‘power’ one should put on CFD in relation to Realism... I think both stands on their own, with or without Bell...

In my mind, counterfactual defiteness should be considered as synonymous with realism, because if the result of a unperformed measurement could not meaningfully spoken of, that means that the act of measurement has no connection with reality, whatever the reality may consist of, whether particles, waves, or anything else.

I The reasoning is correct; however to me kind of ridicules... any “homemade expert” (like me) can construct a LHV that would make it through this “test”... I simply construct a LHV that randomly set my particles to Az = not(Bz) and Ax = not(Bx), I don’t get this at all... no conspiracy as far as I can see...

I don't quite understand what you're saying here. ttn is saying that that if there are only elements of reality for measured attributes then that leads to a violation of no-conspiracy. In other words he's saying that if we have perfect corellations but LHV is false, then no-conspiracy is violated. But you're describing an example where LHV is true, so how does that show anything?

But... this ‘equation’ doesn’t work... you have Realism on both left and right-hand side, with additional ‘values’ on left-hand...

Well, that's just because of how you framed it. I would state it as locality + CFD/realism + no-conspiracy implies LHV. I wouldn't call LHV realism, although it does imply realism.

 

[DevilsAvocado]

Lugita, it’s very late and I have to leave, tomorrow is busy, maybe Monday/Tuesday...

 

[billschnieder]

Elementary my dear Watson, let’s use the Bell parameter of the CHSH inequality:
S = E(a, b) - E(a, b') + E(a', b) + E(a' b')

The "Bell test angles":
a = 0°
a' = 45°
b = 22.5°
b' = 67.5°

Gives:
S = E(0°, 22.5°) - E(0°, 67.5°) + E(45°, 22.5°) + E(45°, 67.5°)

And the relative angles (a-b) are:
S = E(22.5°) - E(67.5°) + E(22.5°) + E(22.5°)

Then calculate for good old Malus classical polarizer cos^2(θ):
S = E(0.85) - E(0.14) + E(0.85) + E(0.85)

And sum up:
S = 2.41

Voila monsieur!

Read carefully:

I challenge anyone to find values for E(a), E(b), E(c), E(d) ∈ [−1,1] that violate the above inequality from any source whatsoever using any means whatsoever (local or non-local).

 

[billschnieder]

It has been suggested recently that Bell's theorem can be formulated without counterfactual definiteness. But let us take a look. The inequality is |C(a,b)−C(a,c)| <= 1+C(b,c). We have three terms here C(a,b), C(a,c), C(b,c). In Bell's theorem, QM is used to calculate correlations for those three terms which when substituted into the inequality lead to a violation. However, let us look more carefully. According to EPR experiment, the three terms do not all commute. They are like sides of a triangle, once you pick one, your choice for the next is restricted and once you pick the first two, there is only one choice left for the third. Therefore there is no way that QM can provide 3 terms without using CFD.

C(a,b) = QM correlation for what we would get if we measure (a,b)
We measure (a,b) and get the result C(a,b), therefore the other two correlations become:
C(a,c) = QM correlation for what we would have gotten had we measured (a,c) instead (ie CFD)
C(b,c) = QM correlation for what we would have gotten had we measured (b,c) instead (ie CFD)

Bell's theorem can not be formulated without CFD. The error then is to assume that the following two correlations below are the same:

(1) C(b,c) = QM correlation for what we would get if we measure (b,c)
(2) C(b,c) = QM correlation for what we would have gotten had we measures (b,c) instead of the (a,b) we measured.

They are not. While correlation (1) does not depend on the result obtained for C(a,b), the second counterfactual correlation does depend on C(a,b) for the simple reason that we have picked one side of the triangle and the result for picking the remaining two sides depends on which side we picked first, without any conspiracy or non-locality.

 

[DevilsAvocado]

not sufficient conditions to evade Bell's theorem, because the photons may not do the right things.

Okay, we have [almost] the same view, still in my version might and may is ‘forbidden words’, all there is in this [stupid] world is; shall, must, forced, determined, etc...

In my mind, counterfactual defiteness should be considered as synonymous with realism,

Slightly different again; CFD comes of course mandatory with realism; the other way is not in my mind not as certain, especially if CFD is put at test with the Schrödinger wavefunction.

In other words he's saying that if we have perfect corellations but LHV is false, then no-conspiracy is violated. But you're describing an example where LHV is true, so how does that show anything?

I’m just saying that this particular ‘proof’ is extremely weak if it attempts to advocate that no-conspiracy is violated, i.e. the particles at source do know in advance what experiments are going to be performed on them later. And I showed you my simple random LHV model that shreds this argument if “either the z-axis or the x-axis is chosen along which to perform the measurements”.

I think that if I can make a classical LHV actually work [in this particular case], that would effectively kill any conspiracy theories, right?

Well, that's just because of how you framed it. I would state it as locality + CFD/realism + no-conspiracy implies LHV.

Okay, now I understand, maybe we could include no-conspiracy in locality [time-like & space-like], and then we get:

Local (causality/no-conspiracy) Hidden Variables (realism/CFD)
LHV ≠ QM

(dBB has non-local hidden variables, do you consider them as violating no-conspiracy or locality?)

I wouldn't call LHV realism, although it does imply realism.

Agreed!

 

[DevilsAvocado]

The error then is to assume that the following two correlations below are the same:

(1) C(b,c) = QM correlation for what we would get if we measure (b,c)
(2) C(b,c) = QM correlation for what we would have gotten had we measures (b,c) instead of the (a,b) we measured.

They are not.

There must be some confusion:

You have E(a), E(b), E(c), E(d) when there is only two (2) measuring apparatus A & B which has only two (2) outcomes +/- for two (2) independent settings a/a' and b/b'. No triples, no triangles.

The ‘triangle’ you talk about is only a hypothetical assumption IF you claim LHV to be true, then you have to have (predetermined) definite values for all possibilities, right? And there’s no wonder you can’t make it work, because it’s mathematically/logically and experimentally proven wrong.

 

[stevendaryl]

Meaning what, exactly?

I think that Bell described the classical notion of local theory in his essay about "The Theory of Local Beables" (the last word is a neologism pronounced bee - able, in contrast to observe -able). Roughly speaking, it assumes that:

Whenever an experiment is performed, the outcome (or probabilities for various outcomes, if it is a nondeterministic theory) is solely a function of facts about conditions and events in the backwards light cone. An implication of this principle is that if distant events are correlated, then there must be some facts about the intersection of their backwards light cones that explain this correlation.

Pictorially, the picture shows two distant events D and E. Region A consists of those events in the (causal) past of D (that is, events that were capable of sending a lightspeed or slower signal to D). Region B consists of the causal past of event E. Region C is the common causal past of D and E.

So the theory of local beables says that if an observation at E allows you to predict something about the results of an observation at D, then the same prediction in principle could have been made using only facts from region C.

Any theory of local beables will satisfy Bell's inequality. (Okay, that's not strictly true, because there are weird counter-examples involving nonmeasurable sets, but I don't think anyone takes them seriously, although I sometimes think about them.)

I should point out that there is a guy, Joy Christian, who claims that Bell's theorem is mistaken, and that it implicitly assumes something about the topology of space, but I have been unable to make any sense of his claims.

 

[DevilsAvocado]

I should point out that there is a guy, Joy Christian, who claims that Bell's theorem is mistaken, and that it implicitly assumes something about the topology of space, but I have been unable to make any sense of his claims.

Don’t worry Steven, some people seriously think it’s Joy Christian who is mistaken...

Quantum Randi Challenge: Help Perimeter Physicist Joy Christian To Collect The Nobel Prize

 

[stevendaryl]

"... Seriously, today there is absolutely no doubt that the EPR argument is invalid.

I don't think that's true at all.

 

[DevilsAvocado]

I don't think that's true at all.

me clumsy, see #465

 

[billschnieder]

There must be some confusion:

You have E(a), E(b), E(c), E(d) when there is only two (2) measuring apparatus A & B which has only two (2) outcomes +/- for two (2) independent settings a/a' and b/b'. No triples, no triangles.

The confusion is on your part. Let us illustrate using your previous example.

You write. S = E(0°, 22.5°) - E(0°, 67.5°) + E(45°, 22.5°) + E(45°, 67.5°)

There are 4 different angle settings
a = 0°
b = 45°
c = 22.5°
d = 67.5°

But only two of them can be measured at the same time as your diagram shows. It still does not change the fact that we have outcomes at 4 angles. For each angle there is an outcome. Wasn't this supposed to be the "Realism" assumption.

Let's show that the result for E(0°, 67.5°) depends on the result for E(0°, 22.5°). Let us consider only the first two photons emitted and then write down their fate for the possible angles in the above expression. We'll use +1 or -1 for the result at each polarizer.

Say for the (0°, 22.5°) experiment we have (+1, -1) for 0° and 22.5° respectively. We then must necessarily have obtained (+1, ?) for (0°, 67.5°) , and (?, -1) for (45°, 22.5°) (where ? represents either +1 or -1). Surely it is common sense to see that if we measured the first photon pair at (0°, 22.5°) and got (+1, -1) , we would have gotten (+1, ?) had we measured at (0°, 67.5°) instead, and we definitely would have gotten (?, -1) had we measured at (45°, 22.5°) instead (Remember CFD). We could repeat this for every pair of photons and it doesn't take rocket science to appreciate the fact that knowing the results of one experiment affects how we calculate the others, therefore the results for the different correlations in the CHSH are interdependent.

The reference to a triangle was while discussing Bell's original inequality which has only 3 terms. As illustrated above, the main point does not change just because you now have the 4-term CHSH.

 

[stevendaryl]

... Maybe I was wooly, but that is exactly what I meant; determinism + no free will = superdeterminism.

I don't like dragging free will into discussions about science, because I just don't think it has any relevance. "Free" choices that humans make could very well be determined by conditions at a microscopic level, and that wouldn't make much difference, in practice. What I thought was the difference between determinism and superdeterminism is this:

• A theory is deterministic if a past state uniquely singles out one possible future state.
• A theory is superdeterministic if there is only one possible past, as well.

Newtonian physics is deterministic, but not superdeterministic. It gives the future positions and velocities of particles in terms of past positions and velocities, but the initial positions and velocities are arbitrary. So there are many possible pasts, but for each possible past, there is exactly one possible future.

A superdeterministic theory would have constraints that single out only one possible initial condition, as well as only one possible future. I can easily imagine what a superdeterministic theory might look like.

For example, suppose that instead of the usual theory that takes an initial state at one point in time and evolves it toward a state at a later point in time, we have a theory that evolves the entire history of the universe in terms of an unobservable "hypertime" parameter. So you start with complete history of the universe, $h_0$, where $h_0(t)$ gives the state of the universe at time $t$. Then you solve the initial-value equations:

$H(t,0) = h_0(t)$
$\dfrac{d}{ds} H(t,s) = G(H(t,s), \frac{\partial}{\partial t} H(t,s))$

Then the "actual" history of the universe is some kind of limit:

$h(t) = lim\ s \rightarrow \infty\ :\ H(t,s)$

It could very well be that such a limit might be independent of the initial choice of $h_0(t)$.

I had the idea that Stephen Hawking worked on an idea like this for the "wave function of the universe". The details of both future and past were fixed by requirements of self-consistency.

 

[billschnieder]

So the theory of local beables says that if an observation at E allows you to predict something about the results of an observation at D, then the same prediction in principle could have been made using only facts from region C.

But the problem with that theory is that if you have the results of the measurement you have already done at A and B with settings (a, b), those results must influence your prediction for what you would have obtained if you were measuring at the angles (a', b') instead (counterfactually).

Traditionally, we have always analyzed the situation as, the result at Alice tells us something about the result at Bob. However, the way we should analyze it is that, the correlation between Alice and Bob at angle pair (a,b), tells us something about what correlation would be obtained had Alice and Bob measured at angle pair (a, b'), or (a', b) instead.

But looking at how Bell's theorem is derived, the same values are used for the correlation for each term without any interdependence requirement. This is a mathematical error. This is related to the measurable sets issue because the terms in the CHSH being counterfactual, are not all simultaneously measurable. So no experiment can ever be done to verify it.

 

[stevendaryl]

But the problem with that theory is that if you have the results of the measurement you have already done at A and B with settings (a, b), those results must influence your prediction for what you would have obtained if you were measuring at the angles (a', b') instead (counterfactually).

Traditionally, we have always analyzed the situation as, the result at Alice tells us something about the result at Bob. However, the way we should analyze it is that, the correlation between Alice and Bob at angle pair (a,b), tells us something about what correlation would be obtained had Alice and Bob measured at angle pair (a, b'), or (a', b) instead.

But looking at how Bell's theorem is derived, the same values are used for the correlation for each term without any interdependence requirement. This is a mathematical error. This is related to the measurable sets issue because the terms in the CHSH being counterfactual, are not all simultaneously measurable. So no experiment can ever be done to verify it.

I'm not exactly sure what you're saying. Are you saying that a local realistic theory can reproduce the predictions of the EPR?

Anyway, Bell's "local beables" are NOT measurements. There is no assumption that any measurements were performed in regions A or B. We're only talking about measurements performed at D and E.

 

[DevilsAvocado]

But only two of them can be measured at the same time as your diagram shows. It still does not change the fact that we have outcomes at 4 angles. For each angle there is an outcome. Wasn't this supposed to be the "Realism" assumption.

Well, there is not “an outcome” for every angle (obviously), but IF you are a proponent of LHV then you must obviously be able to handle any [relative] angle between 0-360° since you are completely ‘helpless’ once at the measuring apparatus, facing the actual random settings. This is a problem for supporters of Local Realism, not for Bell (And how could it be? Bell has proven LHV wrong? We can’t possibly expect Bell to provide a working LHV theory, could we??).

Let's show that the result for E(0°, 67.5°) depends on the result for E(0°, 22.5°). Let us consider only the first two photons emitted and then write down their fate for the possible angles in the above expression. We'll use +1 or -1 for the result at each polarizer.

Say for the (0°, 22.5°) experiment we have (+1, -1) for 0° and 22.5° respectively. We then must necessarily have obtained (+1, ?) for (0°, 67.5°) , and (?, -1) for (45°, 22.5°) (where ? represents either +1 or -1). Surely it is common sense to see that if we measured the first photon pair at (0°, 22.5°) and got (+1, -1) , we would have gotten (+1, ?) had we measured at (0°, 67.5°) instead, and we definitely would have gotten (?, -1) had we measured at (45°, 22.5°) instead (Remember CFD). We could repeat this for every pair of photons and it doesn't take rocket science to appreciate the fact that knowing the results of one experiment affects how we calculate the others, therefore the results for the different correlations in the CHSH are interdependent.

I’m sorry Bill this is where you get it wrong. Every individual outcome at A & B is always 100% random, it does not make any sense imagine static/predetermined results in QM – it’s always a 50/50 chance for getting +1/-1. The only exception is perfect correlations, i.e. at aligned angles, if you first measure A to be +1, then you will know the outcome of B. But then you run into relativistic difficulties in deciding who makes the measurement first (depending on the observer).

You can think of it like this: IF it was possible to ‘control’ the outcome of an EPR-Bell experiment, we could use it to send FTL information! And I hope this not what you are claiming, right...?

Your reasoning about “we then must necessarily have obtained” is a counterfactual definiteness argument, and as we all know Bell’s theorem shows that Realism(CFD) and/or Locality has to go to be compatible with QM. So let’ say we preserve CFD and sacrifice Locality. What happens then? Well, this would mean non-local hidden variables (as in dBB), and ‘something’ is then checking the apparatus settings before the particles leave the source, and this will bring you back to square one, you can’t possible know the outcome if the settings was different.

Trust me.


[To Steven & Co., I have to go now, no time, hopefully back tomorrow]

 

[Ilja]

I should point out that there is a guy, Joy Christian, who claims that Bell's theorem is mistaken, and that it implicitly assumes something about the topology of space, but I have been unable to make any sense of his claims.

His claims do not make sense. He has some strange construction which gives some E(a,b) but has not understood that these E(a,b) are only computed from probabilities p(A,B|a,b), which are observables, and the A, B simply observed values, or +1 or -1.

See my discussion with him at http://fqxi.org/community/forum/topic/812

I have asked you a quite simple question. Again, even simpler: Have you provided, in one of your papers, a local model which predicts probabilities p(A,B|a,b) so that the corresponding expectation values E(a,b)=sum AB p(A,B|a,b) violate Bell's inequalities?

If yes, tell me the paper and the pages. If not, that's my point.

In this case, explain where is the error in my argument. I think the probabilities p(A,B|a,b) are predicted by QM and corresponding frequencies are measured in experiments, in a quite open way, without anything hidden. So any realistic model has to recover them.

What's your problem with explaining me the simple error in such a simple argument? Of course, I have no eyes to see my own errors, else I would not make them. That's a tautology. So, please help a poor soul, who is unable to understand your deep thoughts, to see his trivial error.

Else, I wish you succes with publishing your model in a good journal - it would be a nice possibility for me to receive some explanation of my error by peer review, or to publish a rebuttal there.

In almost all of my papers you will find a local-realistic model that exactly reproduces all of the predictions of quantum mechanics for the singlet state. And by all I mean all. I have no interest in educating you otherwise.

 

[lugita15]

The error then is to assume that the following two correlations below are the same:

(1) C(b,c) = QM correlation for what we would get if we measure (b,c)
(2) C(b,c) = QM correlation for what we would have gotten had we measures (b,c) instead of the (a,b) we measured.

They are not.

Here is what I said to you in an old thread:

I make the crucial assumption, which I expect that you disagree with or think is misleading, that the following two probabilities are always equal:
1. The probability that this photon would go through a polarizer if it is oriented at angle x, given that the polarizer is actually oriented at angle x.
2. The probability that this photon would go through a polarizer if it is oriented at angle x, given that the polarizer is NOT actually oriented at angle x, but instead some different angle y.

Now why do I assume that these two probabilities are equal? Because I am assuming that the answers to the following two questions are always the same:
1. What result would you get if you send this photon through a polarizer oriented at angle x, given that the polarizer is actually oriented at angle x?
2. What result would you get if you send the photon through a polarizer oriented at angle x, given that the polarizer is NOT oriented at angle x, but instead some different angle y?

And why do I assume that these questions have the same answer? That seems to me to be a consequence the no-conspiracy condition: the properties (or answers to questions) that are predetermined cannot depend on the specific measurement decisions that are going to be made later, since by assumption those decisions are free and independent.

 

[billschnieder]

I'm not exactly sure what you're saying. Are you saying that a local realistic theory can reproduce the predictions of the EPR?

I'll leave that up to Joy Christian and the others to figure out. I'm not saying that at all. Rather I'm saying violation of Bell's and CHSH inequalities by QM and Experiments tells us nothing, because the use of correlations from QM and from experiments to compare to the inequalities is deeply flawed. In addition, I'm saying it is impossible to violate the inequalities if you are reasoning correctly even if you assume that non-local causation or any other spooky stuff is happening. The inequalities are mathematical tautologies which apply to all theories, local or non-local!

Anyway, Bell's "local beables" are NOT measurements. There is no assumption that any measurements were performed in regions A or B. We're only talking about measurements performed at D and E.

I meant D and E. Your non-standard choice of notation played one on me. But the argument does not change, just substitute D, and E. I should have said:

But the problem with that theory is that if you have the results of the measurement you have already done at D and E with settings (a, b), those results must influence your prediction for what you would have obtained if you were measuring at the angles (a', b') instead (counterfactually).

Traditionally, we have always analyzed the situation as, the result at Alice tells us something about the result at Bob. However, the way we should analyze it is that, the correlation between Alice and Bob at angle pair (a,b), tells us something about what correlation would be obtained had Alice and Bob measured at angle pair (a, b'), or (a', b) instead.

But looking at how Bell's theorem is derived, the same values are used for the correlation for each term without any interdependence requirement. This is a mathematical error. This is related to the measurable sets issue because the terms in the CHSH being counterfactual, are not all simultaneously measurable. So no experiment can ever be done to verify it.​

 

[stevendaryl]

I'll leave that up to Joy Christian and the others to figure out. I'm not saying that at all. Rather I'm saying violation of Bell's and CHSH inequalities by QM and Experiments tells us nothing, because the use of correlations from QM and from experiments to compare to the inequalities is deeply flawed. In addition, I'm saying it is impossible to violate the inequalities if you are reasoning correctly even if you assume that non-local causation or any other spooky stuff is happening. The inequalities are mathematical tautologies which apply to all theories, local or non-local!

Now I'm completely confused by what you're saying. There is no problem in violating Bell's inequalities if we allow nonlocal causation.

 

[billschnieder]

Now I'm completely confused by what you're saying. There is no problem in violating Bell's inequalities if we allow nonlocal causation.

Are you sure? If you insist, I suppose you can provide a NON-LOCAL dataset of outcomes for three angles a, b, c which violates the inequalities. Using your assumption of non-locality, please generate such a dataset in the form:

a, b, c
-----------
-1, +1, -1
+1, -1, -1
+1, +1, -1
-1, -1, -1
-1, -1, -1
-1, +1, +1
...

For any number of photons you like. Then we will calculate the correlations from it and verify if it violates Bell's inequalities as you claim. Note you can use any assumption you like in generating the outcomes, specifically, please use non-locality and spooky action at a distance. The only condition is there are 3 outcomes for 3 angles for each photon measured.

 

[billschnieder]

Well, there is not “an outcome” for every angle (obviously),

Are you serious? You must have misunderstood something very fundamental about the EPR experiment. For each photon that leaves the source and heads towards Alice, you have a single outcome, (+, -, or non-detection). Alice's polarizer is set to a specific angle say 67.5° for that photon. Same thing for Bob. It is only when Alice has collected all her pluses and minuses and Bob has done the same that they start comparing time-tags to see coincidences and then they can figure out what the angular difference was at the moment of detection! The photon gives no rodent's behind whether Alice's angle was chosen randomly or not! All it meets is a polarizer at a given angle resulting in an OUTCOME of (+, -, or non-detection).

This is a problem for supporters of Local Realism, not for Bell (And how could it be? Bell has proven LHV wrong? We can’t possibly expect Bell to provide a working LHV theory, could we??).

Who talked about expecting Bell to provide a working LHV theory. He assumed LHV from the start, you can't then throw LHV out and then complain that LHV must be wrong because it is not obeyed by what you have left. It is simply called sound reasoning.

I’m sorry Bill this is where you get it wrong. Every individual outcome at A & B is always 100% random

So? Who said any thing about the stream of outcomes appearing at Alice or Bob appearing other than random. That does not change the fact that there is an outcome. I have the files from Weihs' experiment and there is one outcome for each photon detected.

it does not make any sense imagine static/predetermined results in QM – it’s always a 50/50 chance for getting +1/-1.

I'm afraid you have seriously misunderstood. Nobody is assuming static/predetermined results. The result is random for a given photon, but once Alice has measured and obtained +1 for that photon at 67.5°, it is a mathematical/logical error to say Alice would have obtained -1 had she measure that specific photon at the same specific angle 67.5°! You can't set a realism assumption and them immediately gut it and expect it to stay put.

Continuing in next post ...