A Paradox: Do LHV Theories Need the HUP?

[ttn]

I like what you have to say about "if locality is true, there must exist a certain kind of hidden variables which determine the outcomes on each side". That is a great way to frame the argument about local reality. And I agree about the importance of getting EPR and Bell straight, which is why I try to stay close to their words on the subject where possible.
But I disagree about Bell not finding something wrong with EPR. There is something wrong with EPR, and Bell showed it to us!

The thing I said that you liked ("if locality is true, there must exist a certain kind of hidden variables which determine the outcomes on each side") is simply a summary of the EPR conclusion. So I don't see how/why you claim to like this statement, given that you think "there is something wrong with EPR."

EPR said both of the following:
a) Either QM is incomplete, or there is not simultaneous reality to non-commuting observables.

In other words, either QM is incomplete, or it is complete. (Either the two quantities whose simultaneous values are restricted by the HUP are both simultaneously real, or they aren't. If they are real, orthodox QM is incomplete; if they aren't simultaneously real, QM is complete, at least in so far as those two variables are concerned.)

b) They believed that there IS simultaneous reality to non-commuting observables because a more complete specification of the system is possible.

Yes, they argued that there "IS simultaneous reality to non-commuting observables"... but not merely because they felt a more complete specification of the system is possible. That's not a *reason* to believe in the simultaneous reality of those two properties, it's just another way of saying that one believes in the simultaneous reality of those two properties. To believe that a more complete specification of the system is possible is simply to deny the completeness doctrine, specifically, to deny the orthodox view that the uncertainty principle is ontological rather than epistemic.

The *actual reason* EPR believed in the simultaneous reality of these properties is because he saw that to *not* believe in them would violate the assumption of reality. If you think that x and p are not simultaneously real for the distant particle, then, in order to explain the perfect correlations between the particle here and the one there, you *must* posit some kind of non-local mechanism by which the measurement here *causes* the particle there to assume the appropriate, correlated value for the property in question. Completeness entails non-locality (given the predicted correlations). Or equivalently, locality entails in-completeness. Specifically, locality entails that both x and p for that distant particle were already (simultaneously) definite/real before any measurement was made here.

a) was supported by the logic presented. Clearly, b) was not rigorously supported and was an ad hoc assumption. Some people never accepted b) anyway, so it may not be material to them. Maybe that is your opinion too.

Hogwash. You can't be analyzing what's wrong with their argument until you've understood it.

On the other hand, some people did accept b) - but Bell saw a problem with that. He formulated his paper ("On the EPR Paradox") mathematicially assuming there WAS simultaneous reality to such observables, and found that was incompatible with QM itself.

Fine, but you miss what's essential if you just say "some people did accept b)". That's true, but what's important is that people accepted "b)" (which as I noted above is just equivalent to your "a)") *because it was a requirement of locality. The whole point of EPR in so far as it relates to Bell's Theorem is this: given the perfect correlations predicted by QM, the *only* way to respect locality is to deny the completeness doctrine and add local hidden variables to account (locally, duh) for the outcomes. That's the only way you can possibly have a local theory.

Bell later proved that even this way of trying to have a local theory couldn't work. You can't reproduce the QM predictions with a hidden variable theory that respects locality. But this isn't "too bad for hidden variables". To say that is to simply *forget* why we should have believed in hidden variables in the first place, namely: because having them is the only way to have a local theory. That's what EPR showed.

Think of it this way: EPR and Bell both showed that a certain theory (or class of theories) was non-local. EPR pointed out the orthodox QM was nonlocal, and noted what, in principle, would have to be done to construct a local theory. Bell showed that the kind of theory needed to respect locality in the face of the EPR argument, also doesn't work -- such a theory cannot be made to agree with QM/experiment. Conclusion: locality is false. The only way to save it doesn't work.

Hardly a result that EPR envisioned.

No doubt. But that doesn't mean their *argument* is wrong. It means one of the premises of that argument turns out to be untenable. This is elementary logic. "Locality" and "Locality --> InCompleteness" are not the same proposition. EPR accepted the first and proved the second, and hence believed in the conclusion "InCompletness".

Later, Bell proved that this conclusion "InCompleteness" plus the original "Locality" premise entails a contradiction with experiment. So, just considering Bell, either "Incompleteness" or "Locality" must fail. But if "InCompleteness" fails, that means we are upholding the orthodox Completeness doctrine, and that means, per EPR, that we are denying "Locality". So... again... you can't save "locality" by denying "InCompleteness". The two arguments together prove absolutely that "Locality" is false.

(Well, not absolutely... You could always say something completely bonkers, like that we're all deluded when we think that the experiments in question even had definite outcomes. Of course, that would be even crazier than clinging to the various "loopholes" in those experiments that are clung to by fans of local hidden variable theories.)

I would definitely say that EPR took locality as an axiom.

You mean, they took it as a premise in their argument for "InCompleteness"? No doubt. Yet you seem ignorant of the role this premise actually played in the argument.

Bell definitely did not, as he was explicit in this regard.

Excuse me? Are you saying that you don't think "Locality" is a premise of Bell's Theorem? The whole point of the theorem is to show that a certain class of LOCAL theories are inconsistent with the QM predictions.

Or maybe you just mean that, in a broader sense, Bell was willing to consider that possibly "Locality" might be false. That's certain true, although he only thought that because his theorem, combined with the EPR argument, *proved* that "Locality" is untenable.

 

[Sherlock]

But this is making a slanderous implication that experimenters deliberately manipulate their instruments so as to only produce results that will only verify a prevailing idea. Are you willing to stand by such an accusation?
Zz.

Oh come now ZapperZ. Look at what I wrote.

"Bell tests are measuring entanglement. The entanglement is assumed to not vary from entangled pair to entangled pair. Experimenters tweak and calibrate everything to minimize untoward effects. Any variations in the entanglement should be in the results."

What this means is that experimenters do everything they possibly can to ensure that the hardware is working as it should, and that the entanglement preparation is actually producing entangled results.

What are you saying ... that experimenters who conduct Bell tests are *not* trying to produce entangled pairs?

 

[ZapperZ]

Oh come now ZapperZ. Look at what I wrote.
"Bell tests are measuring entanglement. The entanglement is assumed to not vary from entangled pair to entangled pair. Experimenters tweak and calibrate everything to minimize untoward effects. Any variations in the entanglement should be in the results."
What this means is that experimenters do everything they possibly can to ensure that the hardware is working as it should, and that the entanglement preparation is actually producing entangled results.
What are you saying ... that experimenters who conduct Bell tests are *not* trying to produce entangled pairs?

I didn't say anything. I was asking if you're implying that experimenters tweak their equipment to only produce what they think it should. That was how I understood from reading what you said.

And oh, unless I again misunderstood what you are saying, the measurement itself produce only a detection of the component of the entangled variable - it does NOT measure "entanglement". It is only when you look at the whole collection of the measured data can one deduce such such correlation. Other experiments are a lot more convincing in detecting entanglement than the EPR-type experiments (example: the defeat of the diffraction limit by entangled particles).

I'm confused as to why entanglement is the issue here. Even those who are sticking with local realism isn't debating the reality of entanglement. EPR wasn't addressing such a thing, but the non-local nature of entanglement.

Zz.

 

[DrChinese]

The thing I said that you liked ("if locality is true, there must exist a certain kind of hidden variables which determine the outcomes on each side") is simply a summary of the EPR conclusion. So I don't see how/why you claim to like this statement, given that you think "there is something wrong with EPR."
In other words, either QM is incomplete, or it is complete. (Either the two quantities whose simultaneous values are restricted by the HUP are both simultaneously real, or they aren't. If they are real, orthodox QM is incomplete; if they aren't simultaneously real, QM is complete, at least in so far as those two variables are concerned.)
Yes, they argued that there "IS simultaneous reality to non-commuting observables"... but not merely because they felt a more complete specification of the system is possible. That's not a *reason* to believe in the simultaneous reality of those two properties, it's just another way of saying that one believes in the simultaneous reality of those two properties. To believe that a more complete specification of the system is possible is simply to deny the completeness doctrine, specifically, to deny the orthodox view that the uncertainty principle is ontological rather than epistemic.
The *actual reason* EPR believed in the simultaneous reality of these properties is because he saw that to *not* believe in them would violate the assumption of reality. If you think that x and p are not simultaneously real for the distant particle, then, in order to explain the perfect correlations between the particle here and the one there, you *must* posit some kind of non-local mechanism by which the measurement here *causes* the particle there to assume the appropriate, correlated value for the property in question. Completeness entails non-locality (given the predicted correlations). Or equivalently, locality entails in-completeness. Specifically, locality entails that both x and p for that distant particle were already (simultaneously) definite/real before any measurement was made here.
Hogwash. You can't be analyzing what's wrong with their argument until you've understood it.

Fine, but you miss what's essential if you just say "some people did accept b)". That's true, but what's important is that people accepted "b)" (which as I noted above is just equivalent to your "a)") *because it was a requirement of locality. The whole point of EPR in so far as it relates to Bell's Theorem is this: given the perfect correlations predicted by QM, the *only* way to respect locality is to deny the completeness doctrine and add local hidden variables to account (locally, duh) for the outcomes. That's the only way you can possibly have a local theory.
Bell later proved that even this way of trying to have a local theory couldn't work. You can't reproduce the QM predictions with a hidden variable theory that respects locality. But this isn't "too bad for hidden variables". To say that is to simply *forget* why we should have believed in hidden variables in the first place, namely: because having them is the only way to have a local theory. That's what EPR showed.
Think of it this way: EPR and Bell both showed that a certain theory (or class of theories) was non-local. EPR pointed out the orthodox QM was nonlocal, and noted what, in principle, would have to be done to construct a local theory. Bell showed that the kind of theory needed to respect locality in the face of the EPR argument, also doesn't work -- such a theory cannot be made to agree with QM/experiment. Conclusion: locality is false. The only way to save it doesn't work.
No doubt. But that doesn't mean their *argument* is wrong. It means one of the premises of that argument turns out to be untenable. This is elementary logic. "Locality" and "Locality --> InCompleteness" are not the same proposition. EPR accepted the first and proved the second, and hence believed in the conclusion "InCompletness".
Later, Bell proved that this conclusion "InCompleteness" plus the original "Locality" premise entails a contradiction with experiment. So, just considering Bell, either "Incompleteness" or "Locality" must fail. But if "InCompleteness" fails, that means we are upholding the orthodox Completeness doctrine, and that means, per EPR, that we are denying "Locality". So... again... you can't save "locality" by denying "InCompleteness". The two arguments together prove absolutely that "Locality" is false.
(Well, not absolutely... You could always say something completely bonkers, like that we're all deluded when we think that the experiments in question even had definite outcomes. Of course, that would be even crazier than clinging to the various "loopholes" in those experiments that are clung to by fans of local hidden variable theories.)
You mean, they took it as a premise in their argument for "InCompleteness"? No doubt. Yet you seem ignorant of the role this premise actually played in the argument.
Excuse me? Are you saying that you don't think "Locality" is a premise of Bell's Theorem? The whole point of the theorem is to show that a certain class of LOCAL theories are inconsistent with the QM predictions.
Or maybe you just mean that, in a broader sense, Bell was willing to consider that possibly "Locality" might be false. That's certain true, although he only thought that because his theorem, combined with the EPR argument, *proved* that "Locality" is untenable.

I can't really debate what you are saying, as I don't really get your points.

EPR was not about locality: it really isn't discussed and is more a tacit assumption ("... after which time we suppose that there is no longer any interaction between the two parts..."). It was about the completeness of QM. They felt they demonstrated that QM was incomplete. I don't feel they demonstrated that. I feel they DID demonstrate that if QM was complete, then there is not simultaneous reality to non-commuting observables. Do we disagree about this? Or maybe you read the last 2 paragraphs of EPR differently than I do.

Bell discusses locality explicitly ("... the signal involved must propagate instantaneously" ...), as I say. His primary argument, however, has nothing to do with locality and everything to do with reality (i.e. hidden variables) - that is what the math is all about ("It follows that c is another unit vector..."). After then proving that hidden variables are inconsistent with the predictions of QM, he concludes that hidden variables can only be "rescued" within a non-local theory. Do we disagree on this?

It is patently false that EPR+Bell excludes locality. It is also possible that reality is both local and observer dependent (i.e. there is no unit vector c). I am merely stating that QM, per Copenhagen, can be interpreted several different ways and often is.

 

[Sherlock]

I didn't say anything. I was asking if you're implying that experimenters tweak their equipment to only produce what they think it should. That was how I understood from reading what you said.
And oh, unless I again misunderstood what you are saying, the measurement itself produce only a detection of the component of the entangled variable - it does NOT measure "entanglement". It is only when you look at the whole collection of the measured data can one deduce such such correlation. Other experiments are a lot more convincing in detecting entanglement than the EPR-type experiments (example: the defeat of the diffraction limit by entangled particles).
I'm confused as to why entanglement is the issue here. Even those who are sticking with local realism isn't debating the reality of entanglement. EPR wasn't addressing such a thing, but the non-local nature of entanglement.
Zz.

So called "Bell states" are maximally entangled states. Bell inequalities are entanglement 'witnesses'. Violations of Bell inequalities are an indication of the presence of entanglement. Hence, my statement that Bell tests measure entanglement, which, if experimenters have prepared things correctly, is not a *variable* property. The only thing that is varying in the Bell tests (that has anything to do with the outcome) is the joint setting of the polarizers.

Therefore, the application of a hidden variable supplement to the qm formulation is just a *mis*application -- since the variable properties of entangled pairs don't affect the rate of coincidental detection.

The relevant hidden parameter is the entanglement itself, and it isn't varying from pair to pair. So, we can still assume that the entanglement is locally produced at emission.

 

[Sherlock]

Originally Posted by Sherlock
Thus, the statement that Bell test *results* disallow lhv supplements is a bit off. Bell test *setups* disallow lhv supplements -- because such variables as might exist between emitters and detectors are simply not relevant to the results, and including them in the calculation screws it up.

This is definitely not the case. Plenty of experiments have been performed in which the detector settings are changed mid-flight. As a a result, there is no possibility that any kind of equilibrium state (between the emitter and the detector) affects the outcome.

I wasn't talking about any kind of equilibrium state between emitter and detector. Just that the exact properties of each entangled pair will vary somewhat from pair to pair. But this variability will not affect the outcome, as long as the pairs being jointly analyzed are entangled.

Change the joint setting as much as you want while the particles are in flight. It's still that case that for any given pair that's analyzed in a given coincidence interval there is one and only one joint setting that is analyzing the pair -- and a given joint setting that is analyzing entangled pairs will produce a certain predictable rate of coincidental detections.

The point of my statement is that whatever variability there is from pair to pair, this variability isn't relevant to the results. This is one thing that varying the joint analyzer setting randomly while the particles are in flight ensures. But whether the analyzers are varied randomly while the particles are in flight or not, you get the same average results for a given setting -- which is a pretty solid indication that the variable properties of the incident disturbances aren't what is producing the variable results.

So, I take the *entanglement*, per se, as a nonvarying property of the jointly analyzed particles, and then the only variable in the setup is the joint analyzer setting. Hence my statement that the *setup* itself is what disallows a hidden variable supplement to the qm formulation.

 

[vanesch]

It is patently false that EPR+Bell excludes locality. It is also possible that reality is both local and observer dependent (i.e. there is no unit vector c). I am merely stating that QM, per Copenhagen, can be interpreted several different ways and often is.

But nevertheless, it makes us make the rather unconfortable choice between non-locality, and (observed) reality is observer-dependent.
Bohmians (such as, I presume, ttn) and make the first choice, MWIers (like me) make the second choice. Copenhageners do something in between...

 

[vanesch]

Therefore, the application of a hidden variable supplement to the qm formulation is just a *mis*application -- since the variable properties of entangled pairs don't affect the rate of coincidental detection.
The relevant hidden parameter is the entanglement itself, and it isn't varying from pair to pair. So, we can still assume that the entanglement is locally produced at emission.

Yes, of course entanglement is locally produced at emission, that is entirely correct. I'm sorry, and no offense, but I think you never got the "click" of what Bell is all about.
Entanglement is a special kind of state description entirely proper to the formalism of quantum theory, and simply means that the way states of systems are described are, eh, well, entangled, meaning, you cannot disentangle the state description as "the state of A" and "the state of B". I don't know if you realize how revolutionary a concept that is. Never this occurred before in physics. In classical physics, if you have two systems which are in DIFFERENT LOCATIONS, it is always possible to describe the state of the TOTAL SYSTEM as "the state of A" and "the state of B". Of course there can be interactions between these states, and of course these states can have a "common origin" even if they are not interacting, because the systems interacted before.
But "the state of the sun-Betelgeuse system" can always be written as "the state of the sun" and "the state of Betelgeuse". All you can measure about the sun will depend ONLY on "the state of the sun" and all you can measure about Betelgeuse will depend only on "the state of Betelgeuse".
THAT DOESN'T MEAN that there cannot be correlations between both. Indeed, it could be that the sun and Betelgeuse had some interaction long ago, and the correlations of our measurements only measure that "common part" induced by that interaction long ago.
But, as Bell showed, when you have such a separate "this is the state of A" and "this is the state of B" state description EVEN IF THERE WAS A COMMON PART, the correlations you can obtain in such a way have to satisfy certain properties.
This is what is violated in QM. And it is (after the fact) not surprising because the states in QM are NOT of the form "the state of A" and "the state of B". There is only the state of AB.
Again, don't think that this is "simply because they have common origin". Classical systems can have "common origin", but that doesn't deny a reality both to the "state of A" and "the state of B". Measurements on A and B will show statistical correlations, but these correlations WILL SATISFY CERTAIN RULES (like Bell's inequalities). Quantum entanglement goes further and DENIES the existence of a state of A and a state of B.
But people feel uneasy about the fact that there is "no state of A" and "no state of B", and only a "state of AB", because we're used to thinking that what is right here, should have its own 'reality' (state). That's what local reality is all about.
Now it could be that you find it very normal for something NOT to have a state of its own (a reality of its own) just because it is confined to some space. You might have the intuition that "reality is holistic". But it is a very special way of thinking in physics, because VERY MANY USEFUL laws are based upon the locality principle. This is why people like Einstein thought that QM had an UNDERLYING theory which had identical predictions, but which had a (totally different) state description for A and for B. He called those state descriptions "hidden variables".
But Bell's theorem shows that this is not possible.
What is possible is that A and B DO have an individual state description ON THE CONDITION THAT they keep constantly in immediate interaction over long distances. Then, of course, the measurement of one can immediately change the STATE of the other, thus mimicking the quantum result. This is Bohmian mechanics.

 

[DrChinese]

But nevertheless, it makes us make the rather unconfortable choice between non-locality, and (observed) reality is observer-dependent.
Bohmians (such as, I presume, ttn) and make the first choice, MWIers (like me) make the second choice. Copenhageners do something in between...

I hoped you would like my little defense of reality.

I think all the interpretations are uncomfortable at least in some way. And that keeps us on our collective toes!

 

[ZapperZ]

So called "Bell states" are maximally entangled states. Bell inequalities are entanglement 'witnesses'. Violations of Bell inequalities are an indication of the presence of entanglement. Hence, my statement that Bell tests measure entanglement, which, if experimenters have prepared things correctly, is not a *variable* property. The only thing that is varying in the Bell tests (that has anything to do with the outcome) is the joint setting of the polarizers.

Therefore, the application of a hidden variable supplement to the qm formulation is just a *mis*application -- since the variable properties of entangled pairs don't affect the rate of coincidental detection.

The relevant hidden parameter is the entanglement itself, and it isn't varying from pair to pair. So, we can still assume that the entanglement is locally produced at emission.

Then I will await your rebuttal letters to all those experiments that claim that their experiments negate local realism.

Zz.

 

[DrChinese]

Quantum entanglement goes further and DENIES the existence of a state of A and a state of B.

What is possible is that A and B DO have an individual state description ON THE CONDITION THAT they keep constantly in immediate interaction over long distances. Then, of course, the measurement of one can immediately change the STATE of the other, thus mimicking the quantum result. This is Bohmian mechanics.

As you say, a lot of people get tripped up over this point.

If there are non-local hidden variables (in Bell's terms: there is a unit vector c), then there must be a hitherto unknown non-local mechanism in existence as well. After all, you are taking a classical idea - that there are separate A and B systems rather than a combined AB system - and trying to make it give identical predictions to QM. You will need the new hypothetical non-local mechanism to make this happen. Of course, this mechanism must elsewhere be dormant! (Since this mechanism is not explained by QM, QM would necessarily be incomplete if this actually exists. It would also violate special relativity.)

If you believe QM, there is no need (requirement) to postulate Bell's unit vector c. That is because the superposition of states explains it already. So in that limited respect, QM is complete. And since the superposition principle explains everything observed, there is no need for a new non-local mechanism.

(Of course, here I am talking of local and non-local in terms of Bell locality.)

 

[ttn]

I can't really debate what you are saying, as I don't really get your points.

Was something unclear? Or you just don't believe me, despite the logic being clear, or what? I honestly don't understand how you could fail to "get" what I'm saying.

EPR was not about locality: it really isn't discussed and is more a tacit assumption ("... after which time we suppose that there is no longer any interaction between the two parts..."). It was about the completeness of QM. They felt they demonstrated that QM was incomplete. I don't feel they demonstrated that. I feel they DID demonstrate that if QM was complete, then there is not simultaneous reality to non-commuting observables. Do we disagree about this? Or maybe you read the last 2 paragraphs of EPR differently than I do.

Yes, we disagree. First of all, what you are saying makes no sense. "EPR was not about locality... it was about the completeness of QM." The whole point of the EPR argument is to show that ***if*** you assume that QM is complete, the theory violates locality. Completeness entails non-locality.
You say that EPR did succeed in demonstrating that "if QM was complete, then there is not simultaneous reality to non-commuting observables." Do you even understand what you are saying here? There can be no "demonstration" of this statement. It's simply a tautology. The formalism of QM simply doesn't *permit* one to write down a state that attributes simultaneous definite values to non-commuting observables. So if the theory is complete, then those observables really fail to have simultaneous definite values (as opposed to: they have values, but we don't know them).
So, it seems that you think that all EPR proved was an empty tautology -- that if QM is incomplete, then it's incomplete. But that just means you have failed to grasp the actual EPR argument. Now, in your defense, it seems you are overly focused on the EPR paper itself. And that does lead to confusion about this point, because the EPR paper was written by Podolsky and Einstein was rather pissed off about how confusing it was. But we needn't be bothered by any of this, and we needn't remain unnecessarily confused. Einstein made quite clear, many times, later in his life, what the real point of the EPR paper was supposed to have been.

Bell discusses locality explicitly ("... the signal involved must propagate instantaneously" ...), as I say. His primary argument, however, has nothing to do with locality and everything to do with reality (i.e. hidden variables) - that is what the math is all about ("It follows that c is another unit vector..."). After then proving that hidden variables are inconsistent with the predictions of QM, he concludes that hidden variables can only be "rescued" within a non-local theory. Do we disagree on this?

Yes, I don't think you understand Bell's derivation. Look at his paper, "On the EPR Paradox." Right after equation (1) he states openly: "The vital assumption is that the result B ... does not depend on the setting a ... nor A on b." (Check out the footnote, too.) This is the locality assumption. It's only because of the locality assumption that we *forbid* A to depend on b, and vice versa. And without that assumption, the derivation (obviously) does not go through. Bell's inequality is a bound that applies to *local* theories only. So... how you can say "his primary argument...has nothing to do with locality", I have no idea. Again, all I can conclude is that you simply don't understand either EPR or Bell's Theorem. *Both* of these *crucially* involve locality.

It is patently false that EPR+Bell excludes locality.

I can see now how you might think so, since evidently you think that neither EPR or Bell's Theorem has anything to do with locality in the first place!

It is also possible that reality is both local and observer dependent (i.e. there is no unit vector c).

You will have to flesh this out. What, exactly, is "observer dependent"? And please note: if your "observer dependence" includes a dependence of the A-side outcome on the B-side observation, your theory is *nonlocal*. Which means it isn't "both local and observer dependent."
Or was your point that regular old Copenhagen-ish QM is "both local and observer dependent"? That is just patently false. Orthodox QM violates Bell's Locality condition (not the inequality, but the definition of locality that he applies to hidden variable theories in the derivation of the inequality) -- i.e., "regular old Copenhagen QM" is nonlocal. So it isn't an example of a theory that is "local and observer dependent."
In fact, I challenge you to provide any example of a theory that is local, predicts that experiments have definite outcomes, and consistent with the QM predictions. You can include "observer dependence" or anything else you want in the theory as long as it is consistent with Bell Locality. I will be delighted to put my money where my mouth is and make this interesting, if you are game.

 

[ttn]

If there are non-local hidden variables (in Bell's terms: there is a unit vector c), ...

Huh? If you mean the "unit vector c" that appears in Bell's derivation of his inequality, that is not a non-local hidden variable. First off, the lowercase letters in Bell's derivation (in almost all his papers) refer to unit vectors denoting the orientation of Stern-Gerlach devices. The hidden variables are the "lambdas" or, if you prefer (and in the deterministic case), the spin component values A(a,lambda), B(b,lambda), etc.
But my real issue is that, even leaving aside the question of whether you meant lowercase "c" or uppercase "c" or *whatever*, it just doesn't make any sense to talk about non-local hidden variables and cite *anything* from Bell's derivation. The derivation is always talking *exclusively* about *local* theories. If there were non-local hidden variables involved in Bell's derivation of the inequality, it wouldn't exactly be a bound on local hidden variable theories, now would it?

(Since this mechanism is not explained by QM, QM would necessarily be incomplete if this actually exists. It would also violate special relativity.)

But orthodox QM already violates special relativity. The collapse postulate tells us that the quantum state of distant systems can change simultaneously with a nearby measurement. And that "simultaneously" is meaningless according to SR.

If you believe QM, there is no need (requirement) to postulate Bell's unit vector c.

If you believe in locality, you *must* postulate these local hidden variables to account for the correlations.

That is because the superposition of states explains it already. So in that limited respect, QM is complete. And since the superposition principle explains everything observed, there is no need for a new non-local mechanism.

Yes, orthodox QM explains the correlations, but it explains them using a non-local mechanism. The collapse postulate violates relativity.
Of course, you can get around this conclusion if you deny the orthodox completeness doctrine. ...or so it seems until you learn about Bell's Theorem.

 

[DrChinese]

If you believe in locality, you *must* postulate these local hidden variables to account for the correlations.

Yes, orthodox QM explains the correlations, but it explains them using a non-local mechanism. The collapse postulate violates relativity.

I guess I could insult you back, but that wouldn't be nice.

First, assuming "unit vector c" is equivalent to assuming a hidden variable. You can believe in locality and reject the existence of "unit vector c". This is basic logic and is fully compatible with Bell's Theorem. Despite the fact that Bell mentions locality, he did not include it explicitly in his mathematical proof as he did the hidden variable assumption.

Second, QM is as local or non-local as you interpret it to be. This too is basic and why folks argue about Copenhagen vs. Many Worlds vs. Bohmian Mechanics vs. Transactional Interpretation etc. Many scientists feel that QM's collapse postulate is not "non-local" in the sense that no signalling mechanism is violated. So I disagree with you that relativity is violated.

 

[ttn]

I guess I could insult you back, but that wouldn't be nice.

If you think I've misunderstood something, then by all means "insult" me by pointing it out. I won't take it as an insult (as I hope you don't), but as an opportunity to get to the truth on this important issue.

First, assuming "unit vector c" is equivalent to assuming a hidden variable.

Maybe you should clarify your notation, but if it means what I think it means, then you are confused: the unit vector c isn't a hidden variable, it's the direction a certain person measures the spin of a certain particle along. The hidden variable is the "lambda" (Bell's notation) which determines what the *outcome* of that measurement will be.

You can believe in locality and reject the existence of "unit vector c".

Your claim was that the "unit vector c" was a *non-local* hidden variable. Even leaving aside the question of whether it's a hidden variable at all, it isn't non-local. No non-local hidden variables appear in Bell's derivation.

This is basic logic and is fully compatible with Bell's Theorem. Despite the fact that Bell mentions locality, he did not include it explicitly in his mathematical proof as he did the hidden variable assumption.

Look, with all due respect, you have just missed something that is incredibly important. Bell *did* include locality in the proof. See equation (1) of "On the EPR paradox", and the subsequent sentence. Or better yet, see one of his later papers where he makes all of this increasingly clear. I urge you, for example, to read the paper "La nouvelle cuisine" (chapter 24 of the new 2nd edition of Speakable and Unspeakable). Just to give you a taste, here are the titles of the sections from this paper: Introduction, What cannot go faster than light?, Local beables, No signals faster than light, Local commutativity, Who could ask for anything more, Principle of local causality, Ordinary quantum mechanics is not locally causal, Locally explicable correlations, Quantum mechanics cannot be embedded in a locally causal theory, But still we cannot signal faster than light, Conclusion.
Don't you think that suggests that locality was a rather important issue for Bell? But don't believe me -- read the paper.

Second, QM is as local or non-local as you interpret it to be. This too is basic and why folks argue about Copenhagen vs. Many Worlds vs. Bohmian Mechanics vs. Transactional Interpretation etc. Many scientists feel that QM's collapse postulate is not "non-local" in the sense that no signalling mechanism is violated. So I disagree with you that relativity is violated.

I'm sorry, but isn't this just silly naked subjectivism? Would you say that Bohmian Mechanics "is as local or non-local as you interpret it to be"? No way! Bohmian Mechanics is a definite theory, defined by certain equations. If you want to find out if the theory is local or non-local, you just examine the theory carefully and see how it works and assess whether or not it includes non-local physics. There's nothing subjective about this. You don't just close your eyes and inhale incense and wait for a mystical experience to tell you whether it's nonlocal. You just look. And in the case of Bohmian Mechanics, there is no controversy or ambiguity: it's non-local. Specifically, it violates Bell Locality (though it is consistent with "signal locality" -- you can't transmit a message faster than light).
It's the same story with orthodox Copenhagen QM. There's nothing open or unclear. Whether the theory is local or nonlocal isn't a matter of feelings or mystical revelation. You just look at the theory and test: is it consistent with Bell locality? Is it consistent with signal locality? The answers are respectively: no, yes. Same as Bohmian Mechanics. So if you think Bohm's theory violates relativity, you have to think that orthodox QM also violates relativity (on pain of inconsistency). There is nothing to debate here -- just something that needs to be grasped clearly.

 

[DrChinese]

The whole point of the EPR argument is to show that ***if*** you assume that QM is complete, the theory violates locality. Completeness entails non-locality.

Perhaps you would care to provide a quote from EPR that backs this up. FYI, here are the actual last 4 sentences of EPR. Note that the last 3 are now known to be WRONG and this is what got us debating in the first place.

"This makes the reality of P and Q depend on the process of measurement carried out on the first system, that does not affect the second system in any way."

(This is standard Copenhagen interpretation. It is also a way of saying that reality is observer dependent. Please note that this applies equally in any test of QED in which the HUP is used. The HUP tells us that reality IS observer dependent.)

"No reasonable definition of reality could be expected to permit this."

(This is an ad hoc assumption and is not warranted from the argument presented in EPR.)

"While we have thus shown that the wave function does not provide a complete description of the physical reality, we left open the question of whether or not such a description exists."

(This deduction is invalid because the previous sentence is unwarranted. The correct conclusion is that EITHER QM is incomplete, OR there is not simultaneous reality to non-commuting observables. This correct conclusion was stated earlier in EPR.)

"We believe, however, that such a theory is possible."

(Because of Bell, we now know that NO such theory is possible, regardless of Einstein's faith in the matter. R.I.P. Local reality.)

 

[ttn]

Perhaps you would care to provide a quote from EPR that backs this up.

See quant-ph/0404016 for a detailed discussion, including lots of juicy quotes.

FYI, here are the actual last 4 sentences of EPR. Note that the last 3 are now known to be WRONG and this is what got us debating in the first place.
"This makes the reality of P and Q depend on the process of measurement carried out on the first system, that does not affect the second system in any way."
(This is standard Copenhagen interpretation. It is also a way of saying that reality is observer dependent. Please note that this applies equally in any test of QED in which the HUP is used. The HUP tells us that reality IS observer dependent.)

Huh? The point of this sentence you quote is to stress the locality assumption. EPR (i.e., *Podolsky*!) are here pointing out the non-locality implied by the standard "disturbance" view which says: the distant particle doesn't have a definite X or a definite P until the nearby measurement is made, the distant particle then "collapsing" into a state with a definite value for the appropriate operator. Their point is that this non-local collapsing violates locality.

"No reasonable definition of reality could be expected to permit this."
(This is an ad hoc assumption and is not warranted from the argument presented in EPR.)

Substitute "local" for "reasonable" and then it makes perfect sense.

"While we have thus shown that the wave function does not provide a complete description of the physical reality, we left open the question of whether or not such a description exists."
(This deduction is invalid because the previous sentence is unwarranted. The correct conclusion is that EITHER QM is incomplete, OR there is not simultaneous reality to non-commuting observables. This correct conclusion was stated earlier in EPR.)

Blah.

"We believe, however, that such a theory is possible."
(Because of Bell, we now know that NO such theory is possible, regardless of Einstein's faith in the matter. R.I.P. Local reality.)

Agreed. But you still seem to be missing the main point here: EPR showed that orthodox QM violates locality. And that is simply a different point than their belief that a local theory might be possible. They hoped a local theory would be possible, yes. And now we know it isn't, yes. But none of that undermines their argument that orthodox QM (i.e., QM with the completeness doctrine) violates locality. That is, was and always will be true. So it's a mistake to say "RIP Local Reality" as if there was some "non-reality" *alternative* that *was* local. There isn't. Orthodox QM is nonlocal. It violates Bell Locality, which you can just test for yourself if you know how QM works and what Bell Locality means. EPR showed that the only way to save Locality was to reject the completeness doctrine, and supplement QM with some local hidden variables. But then Bell showed that such a LHV theory can't work. So the only way to save locality doesn't work. Locality can't be saved. Locality is false.
That is the real conclusion of this whole EPR + Bell issue, and you'll never see it so long as you bury your head in the sand w.r.t. EPR.

 

[DrChinese]

Maybe you should clarify your notation, but if it means what I think it means, then you are confused: the unit vector c isn't a hidden variable, it's the direction a certain person measures the spin of a certain particle along. The hidden variable is the "lambda" (Bell's notation) which determines what the *outcome* of that measurement will be.

Your claim was that the "unit vector c" was a *non-local* hidden variable.

I don't need to clarify my notation - it is straight from Bell. Please see just after equation (14) where this is introduced. It is axiomatic that vector c exists IF there is SIMULTANEOUS REALITY TO NON-COMMUTING OBSERVABLES. You can call it a hidden variable, hidden observable or anything you want to really. The point is that it maps to what EPR was assuming existed independently of the act of observation.

As presented by Bell, it is neither local nor non-local. This *despite* his statement that particle 1's result does not depend on particle 2's setting, and vice versa. Sure, this matters to the final conclusion (please don't misquote me on this point) but it is not part of the formal proof. Please note that a reasonable person could read Bell's words and conclude that he believes that Bohmian mechanics is the only possible solution to the conclusion he arrives at. Clearly, BM is not the same as QM! Yet, the fact is, today Bohmian mechanics is not really pursued too seriously. Why is that? Because there is absolutely no need to add anything to QM to fit with experiment.

 

[DrChinese]

That is the real conclusion of this whole EPR + Bell issue...

I'm waiting for the quotes. Meanwhile, please continue to give yourself pats on the back.

Meanwhile, on the original subject of this thread: can a local realistic theory (such as S.E.D. - see Vanesch's earlier references) operate without incorporating non-classical ideas such as the HUP or the projection postulate?

As a result of Bell, we now know that LHV theories cannot replicate all of the results of QM. With this knowledge in hand, my curiously was piqued. Presumably, there must be other areas in which the ideas of QM conflict with various fundamental elements of LHV theories. And sure enough, there is work being done to further distance QM from such theories. It turns out that attempts to present LHV theories consistent with Bell tests have not been going very well.

 

[ttn]

I don't need to clarify my notation - it is straight from Bell. Please see just after equation (14) where this is introduced. It is axiomatic that vector c exists IF there is SIMULTANEOUS REALITY TO NON-COMMUTING OBSERVABLES. You can call it a hidden variable, hidden observable or anything you want to really. The point is that it maps to what EPR was assuming existed independently of the act of observation.

I'm sorry, but none of this makes any sense. The lowercase a, b, and c refer simply to directions in space. They are the directions along which some hypothetical S-G apparatus is oriented to measure the spin component (along that direction) of an electron.

But if you think "c" is a hidden variable that has something to do with there being "SIMULTANEOUS REALITY TO NON-COMMUTING OBSERVABLES", there's really no point arguing further with you about this. You obviously just haven't seriously tried to understand Bell's paper(s).

Clearly, BM is not the same as QM! Yet, the fact is, today Bohmian mechanics is not really pursued too seriously. Why is that? Because there is absolutely no need to add anything to QM to fit with experiment.

Apparently the reason Bohmian Mechanics isn't pursued more seriously is that, like you, there are a lot of physicists out there who are seriously confused about these issues. Bohm's theory *shouldn't* be pursued because it conflicts with relativity, right? Oh, but we don't need to worry about the fact that orthodox QM also conflicts with relativity -- that's just a subjective interpretation. Yeah, right. Good physics.

 

[ttn]

I'm waiting for the quotes.

OK, fine, here's one:

"...the paradox [EPR] forces us to relinquish one of the following two assertions:

1. the description by means of the psi-function is complete

2. the real states of spatially separated objects are independent of each other

...it is possible to adhere to (2) if one regards the psi-function as the description of a (statistical) ensemble of systems (and therefore relinquishes (1) ). However, this blasts the framework of the 'orthodox quantum theory.'"

-Albert Einstein, "Reply to Criticisms", from Schilpp (Albert Einstein: Philosopher Scientist), pg 681.


As I said, see quant-ph/0404016 for a more detailed discussion.

Meanwhile, on the original subject of this thread: can a local realistic theory (such as S.E.D. - see Vanesch's earlier references) operate without incorporating non-classical ideas such as the HUP or the projection postulate?

I don't really have any interest in that question, since I don't think local realistic theories are viable. They're refuted by Bell's theorem, so who really cares what weird ideas they can or can't incorporate? Well, not me.

As a result of Bell, we now know that LHV theories cannot replicate all of the results of QM.

True. But an equally important point is: As a result of Einstein, we now know that orthodox quantum mechanics is not local.

 

[DrChinese]

... As a result of Einstein, we now know that orthodox quantum mechanics is not local.

No quote provided from EPR, as I said you won't be able to provide one which is relevant. EPR is about the reality of observables, and so is Bell. You know, is the moon there when no one is watching? If it was, then you could use information from an observation on one entangled particle to augment your knowledge of the other. But that doesn't happen, because there are limits to what we can know about any particle (entangled or not). So I guess I would ask you: does a single particle have a well defined position AND momentum simultaneously? If the answer is NO, then the results of Bell tests shouldn't seem surprising. Entangling them does not change this basic fact. Separating them also does not change this basic fact.

I cannot imagine too many scientists agreeing with your statement above. As a result of EPR, there was no significant change in the view of QM by the founders/followers of QM. You need to re-read the source papers and drop your bias. You can find them on my site if you don't have them: http://www.drchinese.com/David/EPR_Bell_Aspect.htm

And I'm not sure why you are hanging out in this thread if you are not interested in the subject matter.

 

[ttn]

You need to re-read the source papers and drop your bias.

Oh please. This discussion proves that you don't know the literature. I'm perfectly familiar with the "source papers" -- including the EPR paper itself and Bell's first proof of Bell's Theorem. But unlike you, I'm also quite familiar with the rest of the literature on this topic, both "source" and "secondary".

And I'm not sure why you are hanging out in this thread if you are not interested in the subject matter.

You made some false and misleading statements about EPR. Since you seem to comment on this topic a lot, I thought you might be interested to get straight on a few things. But that is apparently not the case... which leaves me with very little reason for continuing to hang out on this thread.

 

[DrChinese]

Moving on to a hopefully more productive discussion...

I have been reviewing Zz's reference on the state of the art in EPR and Bell written by Genovese. This monster has 504 references and is 78 pages long. It covers the history of EPR/Bell plus the state of the art in experiments; plus a discussion of the hypothetical loopholes.

Amazingly, virtually every LHV theory designed to be compatible with Bell test results has been eliminated. As detection efficiency has increased, there has been no degradation in the violations of Bell inequalities. It had previously been postulated that experiments ruling out of LHV theories might be flawed in some respects. While simultaneous elimination of all "loopholes" has not yet occurred, it is getting closer.

No amount of testing has yet indicated that locality vs. non-locality is an issue. I.e. changing the settings of polarizers mid-flight has no influence whatsoever on the results. In addition, no amount of testing has indicated that the sample size has any effect on the outcome. I.e. the detection efficiency is not a variable in the results in any experiment performed so far. However, the goal is to get a detection efficiency in excess of about 81% while simultaneously making random changes in the polarizer settings mid-flight. This is proving to be a difficult goal to achieve.

 

[DrChinese]

Genovese has also acknowledged the difficulty in getting all controversy removed from discussion of experimental results. In his opinion, the ultimate experiment might be performed within the next generation. Yet, even this would be unlikely to silence all voices on the subject.

Regardless, the door would still be open for non-local HV theories which would be possible alternatives to QM. So he expects there will be plenty to investigate for many years to come.

The shear amount of work that has been done in this area in recent years is absolutely astonishing to me. When Bell wrote his paper, he had trouble getting anyone to give it serious attention. Today, interest in the EPR Paradox and Bell's Theorem has never been greater. The advent of PDC technology has even made table-top tests in undergraduate settings possible.

 

[DrChinese]

One might wonder what I mean when I say that there are LHV theories compatible with Bell test results. Obviously, LHV theories are NOT compatible with the predictions of QM. And all tests to date soundly support QM. However...

There are those who hold out hope that QM is simply wrong. This is a difficult position to maintain given current experiments, but that does not stop diehard supporters of LHV theories.

Bell has already pointed out a substantial burden on LHV theories - the Bell Inequality. So if you assume that there is local reality, you are saying in essence that there is something that causes the experimental results to appear to support QM. Thus:

f(experiment) - f(LR) = f(experimental error/loopholes/etc.)

and yet:

f(experiment) - f(QM) = 0 as efficiency increases (frequently at the hundreds of Std Deviation level).

These equations are becoming increasing more difficult to explain for the local realist. Why - if QM is wrong - is it the exact result you get in every experiment? Why - if there are loopholes - is there no variation in results when any single loophole is closed?

It is almost as if someone is arguing that the Earth is 70,000,000 miles from the sun while experiments all say it is 93,000,000 miles away.

In addition, there are other burdens on LHV theories. After all, they need to explain all of the things that QM does too. Double slit, uncertainty, quantum model of the atom, etc. Is it possible that another competing theory could ever jump through all of these hoops?

 

[vanesch]

Yes, I don't think you understand Bell's derivation. Look at his paper, "On the EPR Paradox." Right after equation (1) he states openly: "The vital assumption is that the result B ... does not depend on the setting a ... nor A on b." (Check out the footnote, too.) This is the locality assumption. It's only because of the locality assumption that we *forbid* A to depend on b, and vice versa.

Well, a way of sneaking out is to say simply that there WAS no result at A, until it got transported at b. That A still contained both possible results, and that it was only decided upon when the signal arrived at b.

And without that assumption, the derivation (obviously) does not go through. Bell's inequality is a bound that applies to *local* theories only. So... how you can say "his primary argument...has nothing to do with locality", I have no idea. Again, all I can conclude is that you simply don't understand either EPR or Bell's Theorem. *Both* of these *crucially* involve locality.

This is correct, but they also assume that a measurement at A had a definite outcome.

You will have to flesh this out. What, exactly, is "observer dependent"? And please note: if your "observer dependence" includes a dependence of the A-side outcome on the B-side observation, your theory is *nonlocal*. Which means it isn't "both local and observer dependent."

What is observer-dependent is what the observer at b *learns* from what was supposed to be measured at a. He learns something about b and thinks that this was the "definite" result at A. But the observer at a might just "learn" something quite different about exactly that same outcome (in that case he'll be living in a different branch).

Or was your point that regular old Copenhagen-ish QM is "both local and observer dependent"? That is just patently false.

Orthodox Copenhagenish QM is both observer dependent and non-local in its mechanism.

In fact, I challenge you to provide any example of a theory that is local, predicts that experiments have definite outcomes, and consistent with the QM predictions.

*that* is impossible of course. So you shoot on the one you like least. As I said, it's a hard choice to have to let go either one of the 3 ; I take out the one in the middle, you take out the first one, and the LR crowd takes out the third one.

 

[DrChinese]

What is observer-dependent is what the observer at b *learns* from what was supposed to be measured at a. He learns something about b and thinks that this was the "definite" result at A. But the observer at a might just "learn" something quite different about exactly that same outcome (in that case he'll be living in a different branch).

Looking at it from the point of view of MW:

Bell's derivation is fully consistent with a MW interpretation in the sense that in MW, each branch contains only the actual outcomes. There is no c outcome in a branch in which a and b are measured. This exactly corresponds to Bell's proof.

It is true that Bell incorporates the idea that the setting at A does not affect the outcome at B. (For this to matter, there has to be a mechanism for this to take place.) BUT... In MW, this is not an issue because the main premise - that an observation could have been made at setting c - is explicitly false. A setting at c would be a different branch, and you cannot have settings at a, b and c simultaneously.

 

[Sherlock]

Yes, of course entanglement is locally produced at emission, that is entirely correct. I'm sorry, and no offense, but I think you never got the "click" of what Bell is all about.
Entanglement is a special kind of state description entirely proper to the formalism of quantum theory, and simply means that the way states of systems are described are, eh, well, entangled, meaning, you cannot disentangle the state description as "the state of A" and "the state of B". I don't know if you realize how revolutionary a concept that is. Never this occurred before in physics. In classical physics, if you have two systems which are in DIFFERENT LOCATIONS, it is always possible to describe the state of the TOTAL SYSTEM as "the state of A" and "the state of B". Of course there can be interactions between these states, and of course these states can have a "common origin" even if they are not interacting, because the systems interacted before.
But "the state of the sun-Betelgeuse system" can always be written as "the state of the sun" and "the state of Betelgeuse". All you can measure about the sun will depend ONLY on "the state of the sun" and all you can measure about Betelgeuse will depend only on "the state of Betelgeuse".
THAT DOESN'T MEAN that there cannot be correlations between both. Indeed, it could be that the sun and Betelgeuse had some interaction long ago, and the correlations of our measurements only measure that "common part" induced by that interaction long ago.
But, as Bell showed, when you have such a separate "this is the state of A" and "this is the state of B" state description EVEN IF THERE WAS A COMMON PART, the correlations you can obtain in such a way have to satisfy certain properties.
This is what is violated in QM. And it is (after the fact) not surprising because the states in QM are NOT of the form "the state of A" and "the state of B". There is only the state of AB.
Again, don't think that this is "simply because they have common origin". Classical systems can have "common origin", but that doesn't deny a reality both to the "state of A" and "the state of B". Measurements on A and B will show statistical correlations, but these correlations WILL SATISFY CERTAIN RULES (like Bell's inequalities). Quantum entanglement goes further and DENIES the existence of a state of A and a state of B.
But people feel uneasy about the fact that there is "no state of A" and "no state of B", and only a "state of AB", because we're used to thinking that what is right here, should have its own 'reality' (state). That's what local reality is all about.
Now it could be that you find it very normal for something NOT to have a state of its own (a reality of its own) just because it is confined to some space. You might have the intuition that "reality is holistic". But it is a very special way of thinking in physics, because VERY MANY USEFUL laws are based upon the locality principle. This is why people like Einstein thought that QM had an UNDERLYING theory which had identical predictions, but which had a (totally different) state description for A and for B. He called those state descriptions "hidden variables".
But Bell's theorem shows that this is not possible.
What is possible is that A and B DO have an individual state description ON THE CONDITION THAT they keep constantly in immediate interaction over long distances. Then, of course, the measurement of one can immediately change the STATE of the other, thus mimicking the quantum result. This is Bohmian mechanics.

Something did 'click' for me after I read this. It suddenly became clear to me why Bell *had* to use the form that he did. I don't really know if it's entirely due to the way you laid it out here, but this certainly had the effect of making me realize that at least one aspect of how I had been thinking about Bell-EPR consideration was wrong. So, I appreciate your efforts, as well as other mentors and advisors, here and in other threads. And, don't worry about offending -- some humiliation is part of learning.

 

[vanesch]

Looking at it from the point of view of MW:
Bell's derivation is fully consistent with a MW interpretation in the sense that in MW, each branch contains only the actual outcomes. There is no c outcome in a branch in which a and b are measured. This exactly corresponds to Bell's proof.

Yes, but that could be considered not sufficient, because you can consider the branch of that single observer that has done a lot of measurements, in different directions, and who would then have to conclude that in HIS branch, there seems to be something statistically fishy (as long as we suppose that there is some "free will" to set the polarizers - but let's for the moment not go into that mine field!) with his data.
I think the real point in MW is that when A has her results, but didn't learn yet from B what were the results at B, these results (with Bob and everything included) are still in a superposition. It is only when Bob gets to A, and tells Alice the result, that Alice "joins" one of the two possible branches of B (the two terms of the superposition). But this happened LOCALLY (at Alice's place). Now Alice will conclude from that that Bob DID have a result when he was far away, and that that result seemed fishy, but in fact, Bob DIDN'T have a result: he was in a superposition. So there is influence all right of Alice's settings on what she THINKS Bob measured (when she extrapolates back in time), but that influence was transmitted LOCALLY when Bob in superposition got to Alice and told her (in fact, when the TWO Bobs came to Alice, and Alice only saw one! The one that fitted her settings and result).
So YES, there is an action of Alice's settings on "Bob's" results, but we think that this happens when Bob does his measurement, and in fact it only happens when Bob tells Alice (when Alice chooses which Bob she will see!).
This is what circumvents Bell's theorem: there IS an action of the settings of Alice on "Bob's results" (but it is not at a distance! It happens when Bob tells Alice).

 

[Sherlock]

Yes, of course entanglement is locally produced at emission, that is entirely correct.
...
... as Bell showed, when you have such a separate "this is the state of A" and "this is the state of B" state description EVEN IF THERE WAS A COMMON PART, the correlations you can obtain in such a way have to satisfy certain properties.
This is what is violated in QM. And it is (after the fact) not surprising because the states in QM are NOT of the form "the state of A" and "the state of B". There is only the state of AB.
Again, don't think that this is "simply because they have common origin".

Please critique these statements and line of reasoning:
1. Bell tests are testing the viability of a certain general formulation wrt correlations of spatially separated quantum measurements involving entangled particles.
2. This general formulation involves the assumption (local realism) that the correlations can be adequately described in terms of the juxtaposition of the physical evolutions of the individual particles, A and B, of any and all entangled pairs.
3. In qm there is no description of the physical evolution of the individual particles, and due to HUP such a description is impossible in principle.
4. In qm, because there is no description of the physical evolution of the individual particles, but because the average joint results can be quantitatively reproduced, the state of the system is described holistically. That is, as the nonseparable, AB, state.
5. The entangled, qm nonseparable, state is locally produced at emission.
6. The correlations are produced via common settfings of spatially separated analyzers.
7. The observed predictable variations in the correlations occur because, i) the paired -- entangled -- particles have a common source, and ii) the paired particles are being analyzed by a common instrumental variable.
8. To date, the qm description of nonseparable states is quantitatively accurate, and the qm canon that a description of the physical evolution of individual particles is limited by HUP, and therefore that a complete description of such evolution is in principle impossible, is confirmed.
9. Since local realist theories are, to date, not quantitatively accurate, and since in order to match the quantitative accuracy of the qm formulation they would seem to require a more complete specification of the physical evolution of entangled particles than is physically possible according to qm, then *assuming* that the fundamental quantum of action is a universal limiting factor, then it can be concluded that the local realist form is, in principle, disallowed.

And, this tells us nothing about whether or not there are superluminally propagating disturbances in nature, or whether or not there is a reality independent of our observations.

 

[vanesch]

Please critique these statements and line of reasoning:
1. Bell tests are testing the viability of a certain general formulation wrt correlations of spatially separated quantum measurements involving entangled particles.

Bell tests verify whether the correlations found in spatially separated systems respect of violate Bell locality conditions, where Bell locality conditions are the conditions that come from NON-QUANTUM local realist theories. Local realist theories are a class of theories that assign a reality (a definite state) to each local system individually, and the outcome of ANY experiment on that local system is purely determined by that local state. So a Bell test has a priori NOTHING to do with quantum theory. It tests whether certain correlations could eventually be produced by a theory within the class of Local Realist theories.
We only use quantum theory (which is NOT a LR theory) to hint us where to look for VIOLATIONS of these conditions, and then do the experiments accordingly.

2. This general formulation involves the assumption (local realism) that the correlations can be adequately described in terms of the juxtaposition of the physical evolutions of the individual particles, A and B, of any and all entangled pairs.

Entangled or not. Because that's not the LR business. But the Bell tests are of course only INTERESTING with entangled quantum systems, as in this case, QM predicts violation of the Bell conditions. In non-entangled quantum systems, QM does NOT violate the Bell conditions, so we expect the Bell test to be satisfied (and hence allow for a LR theory). This is not interesting.

3. In qm there is no description of the physical evolution of the individual particles, and due to HUP such a description is impossible in principle.

I don't know if it is the HUP which does this. I would say that it is the core principle of quantum theory which does it: the superposition principle.

4. In qm, because there is no description of the physical evolution of the individual particles, but because the average joint results can be quantitatively reproduced, the state of the system is described holistically. That is, as the nonseparable, AB, state.

Yes. I could make a comment, but I'm affraid it would lead us away from the main topic.

5. The entangled, qm nonseparable, state is locally produced at emission.

Yes.

6. The correlations are produced via common settfings of spatially separated analyzers.

"produced" is maybe a bad choice of words. I'd say, that you can calculate the expected correlations of the measurements in QM, by considering a "common measurement" operator which describes the two settings of the two analysers, applied to the "holistic state" AB.

7. The observed predictable variations in the correlations occur because, i) the paired -- entangled -- particles have a common source, and ii) the paired particles are being analyzed by a common instrumental variable.

In the quantum formalism, the correlations are indeed, as I said, the result of applying a "holistic" observable (containing the two settings of the two analysers) to the "holistic state" (the entangled pair). I don't know if that is what you are saying.

8. To date, the qm description of nonseparable states is quantitatively accurate, and the qm canon that a description of the physical evolution of individual particles is limited by HUP, and therefore that a complete description of such evolution is in principle impossible, is confirmed.

Let's simply say that there are 2 results:
1) purely theoretically: Bell's theorem tells us that the ("holistically calculated") correlations we can CALCULATE in QM violate the Bell conditions for certain, entangled, states. As such, we already know that there can be no LR theory which makes, in all cases, identical predictions as QM. That's without any discussion (although some try to do so).
2) experimentally: it could of course simply be that QM is experimentally wrong in these cases. However, there are many experimental results which suggest very strongly that the quantum predictions are correct, even in those cases where QM predicts violation of the Bell locality conditions. The reason why I'm using a cautious tone is just for the sake of not being rebutted by "loophole finders", because indeed, for (to my knowledge) every experiment, there are "loopholes" in the setup, which allow LR proponents to 'save their ass'. These loopholes result from the fact that the setup is complicated and that you need to apply correction techniques (such as subtraction of background, and taking into account efficiencies - things that are usually accepted as standard experimental techniques).
So from the LR-proponent side, yes, we don't have ultimate experiments without any correction that show in the raw data clear Bell locality violations. We only obtain that with standard corrections of experimental techniques.
From the QM-proponent side, these measurements are awfully close to what standard QM predicts, including the prediction of the experimental corrections. So at least, QM is not falsified, even when it is used in the domain where its states predict ideally violations of Bell locality conditions.

9. Since local realist theories are, to date, not quantitatively accurate, and since in order to match the quantitative accuracy of the qm formulation they would seem to require a more complete specification of the physical evolution of entangled particles than is physically possible according to qm, then *assuming* that the fundamental quantum of action is a universal limiting factor, then it can be concluded that the local realist form is, in principle, disallowed.

I think this is badly formulated. Local realist theories are not "quantitatively inaccurate". We don't consider specific examples of LR theories. We know that ALL of them need to respect the Bell locality conditions, so we already know that they can never give identical results in all cases as QM.
But the reason is not that QM has a "less complete specification", or that this would "violate the HUP" or something. In fact, a priori, there would be nothing against a totally different theory, that allowed for "more complete state specifications" and would overthrow the HUP, as long as it made the same statistical predictions (statistical because of our ignorance of this "more complete part" - the hidden variables) as QM. This was in fact what Einstein was hoping for. What kills such a possibility is not QM's axioms of course (because we're talking about a DIFFERENT theory, with identical outcomes). What kills it is the fact that such a theory can never make identical predictions, as it has to respect Bell conditions, which are violated by QM.
However, if you drop the Locality condition, then you CAN construct a theory with a more complete specification of the state, which DOES assign individual reality to the systems A and B, and which makes identical predictions as QM. That theory exists, is known, and is called Bohmian mechanics.
Bohmian mechanics looks a lot like classical mechanics, except that there are forces at a distance (non-local dynamics). It makes identical predictions with QM. But it is of course NOT relativistically invariant in its mechanism.

And, this tells us nothing about whether or not there are superluminally propagating disturbances in nature, or whether or not there is a reality independent of our observations.

No, but at least it tells us that you cannot have both, in the way they were assumed in a LR theory. One thing has to give.

 

[Sherlock]

And, this tells us nothing about whether or not there are superluminally propagating disturbances in nature, or whether or not there is a reality independent of our observations.

No, but at least it tells us that you cannot have both, in the way they were assumed in a LR theory. One thing has to give.

I'm just saying that the Bell issue isn't telling us anything about nature, which you seem to agree with. Is that correct?

Thanks for the extended comments. I'm redoing my list of statements, and will resubmit (until I get it right :-) ). Is this thread ok for that or should I start a new one?

 

[vanesch]

I'm just saying that the Bell issue isn't telling us anything about nature, which you seem to agree with. Is that correct?

It tells us something about quantum mechanics. Whether quantum mechanics describes nature is another issue, but it tells us that, concerning a combined set of properties one would like to have, and which quantum mechanics doesn't possess, namely local reality, you will never find ANOTHER theory which does have these property (local reality) and which has identical predictions in all circumstances as quantum theory.
In as far as experiments seem to confirm the QM predictions for exactly these cases, I would say that it DOES tell us something about nature, namely that local reality, in the way it is imagined in the kind of theories considered by Bell, is not valid in nature.

However, I do not agree with the shortcut that people take, and that say that, for instance, Bell disproves *locality*. This is not correct, as there exists a version of QM that is local, namely MWI (but MWI does not assign any reality to the outcomes of remote measurements). Bell does not disprove either what one could call "reality" (or even determinism). Indeed, Bohmian mechanics is such a theory (but it contains non-local dynamics).

 

[ttn]

However, I do not agree with the shortcut that people take, and that say that, for instance, Bell disproves *locality*. This is not correct, as there exists a version of QM that is local, namely MWI (but MWI does not assign any reality to the outcomes of remote measurements). Bell does not disprove either what one could call "reality" (or even determinism). Indeed, Bohmian mechanics is such a theory (but it contains non-local dynamics).

Well, I'm one of the people who take the "shortcut" of saying that locality has been disproven (by some combination of EPR and Bell and experiment). So we might as well be clear on exactly what it is that is cut short -- i.e., exactly what other tacit premises are really needed to justify the claim that locality as such is refuted.
It's pretty simple and, Patrick, I'm pretty sure you and I agree about this: the other premise that you need is the idea that for each photon pair in the experiments, the measurements on both sides *have definite outcomes*. That is, for any incoming photon pair, both Alice and Bob see definitely either spin up or spin down (along whatever direction is being measured at that moment) for their photon. In particular, Alice has to say: I know Bob just made a measurement and I don't know yet what the outcome of that measurement was, but I know it had some one particular definite outcome.
If one accepts this, then there is no way around the conclusion that locality is false. Anyone disagree with that?
Now what does it mean to accept this extra premise? Is this some kind of weird thing to believe in? Is it tantamount to adding extra variables to QM or believing in epicycles or cold fusion or homeopathy? I'd be curious what others think.