Local realism ruled out? (was: Photon entanglement and )

[Frame Dragger]

Demystifier,

I am happy you understood me. Thank you.

So now the question is whether mathematical rigor is relevant to our discussion.

You see, I can live with nonlocality, no problem at all. I'm just curious: why should I?

You mentioned the real world. However, there is no signal nonlocality in the real world, no experimental demonstration of violations of the genuine Bell inequalities. So we are left with no-go theorems, such as the Bell theorem. But if it uses approximations as assumptions, that opens a hole for locality. Is this hole wide enough or too narrow? I don't know. Do you?

Quantum theory is mature and astonishingly precise, so we can and should judge it to the highest standards. Classical mechanics also was mature and astonishingly precise (and nonlocal, by the way, what with Newton gravity and things like that). But it had problems with birth control, so relativity and quantum theory were born. So is the Bell condom good enough to avoid the trouble of locality? I don't know. The only thing I know it has holes, both experimental and theoretical.

As for my leaving or not leaving physics... You see, physics is a very wide area, there is enough place there both for approximations and for rigorous results, for the Boltzmann equation and for Poincare recurrence theorem. You were very kind to call one of my ideas "interesting", and I am grateful to you, but that idea was based on a rigorous result. Actually, we all do what we can, not what we want.

A question answered with a question devoid of any SEMBLANCE of new thinking or information? Oh wait, it was said in the MAXIMUM (ok, near max) number of words possible... what a shock.


Tell you what, since you're repeating yourself, go back and re-read the last few question Dr. Chinese has asked you, and answer them in order. As for leaving physics, I think it's a given you were never there based on your lack of responses, and the simple fact that if this is how you comported yourself, you would have been beaten to death by nerds.

 

[akhmeteli]

You manage to write a lot of words and make a lot of empty claims. I am certainly glad you agree with yourself, very impressive that. Meanwhile, quit making unsupported claims. Where is there a paper which says that Bell assumes UE or PP? HOW ABOUT A BONA FIDE DIRECT REFERENCE FROM A RESPECTED SOURCE?

DrChinese, thank you for your time and your letters, I do appreciate them. Actually, they are quite helpful.

Unfortunately, I cannot answer all your questions immediately. I'll try to do it later, but let me start somewhere. So here's the reference:

E. Santos, "Bell’s theorem and the experiments: Increasing empirical support for local realism?", Studies in History and Philosophy of Modern Physics, 36 (2005) 544–565. It's mostly Section 7.

Some quotes:

"According to the traditional formulation, quantum mechanics consists of two quite different ingredients: the formalism (including the equations) and the theory of measurement, both of which are postulated independently. (Actually the two ingredients are to some extent contradictory, because the quantum evolution is continuous and deterministic except during the measurement, where the ‘‘collapse of the wavefuction’’ is discontinuous and stochastic. Thus the modern approach tends to remove any postulated theory of measurement...)."

"The point is that standard proofs of ‘‘Bell’s theorem’’ rest upon the theory of measurement (and preparation of states)."

Santos then mentions other elements of the measurement theory than PP, but you do need PP to calculate the correlations for quantum mechanics: say, you measure a spin projection of one particle of the entangled pair, say, you get value +1, then you use PP to state that after the measurement the system has a definite spin projection of the first particle, then you use UE to state that, due to conservation of angular momentum, the spin projection of the other particle on the same axis is -1, and only then you use the Born rule to find the probability of the other particle having a certain projection of spin on another axis. As the two measurements are spatially separated, it does not matter if you conduct one measurement earlier than the other, later, or simultaneously.

So you cannot take the Malus law from nowhere. It cannot appear in the proof of the Bell's theorem as an experimental law, it can appear there only as a derived result of quantum mechanics, otherwise you cannot say that quantum mechanics predicts nonlocality. And to derive the Malus law in quantum mechanics, you need the theory of measurement, e.g., PP (as I described above).

 

[DrChinese]

DrChinese, thank you for your time and your letters, I do appreciate them. Actually, they are quite helpful.

Unfortunately, I cannot answer all your questions immediately. I'll try to do it later, but let me start somewhere. So here's the reference:

E. Santos, "Bell’s theorem and the experiments: Increasing empirical support for local realism?", Studies in History and Philosophy of Modern Physics, 36 (2005) 544–565. It's mostly Section 7.

Some quotes:

"According to the traditional formulation, quantum mechanics consists of two quite different ingredients: the formalism (including the equations) and the theory of measurement, both of which are postulated independently. (Actually the two ingredients are to some extent contradictory, because the quantum evolution is continuous and deterministic except during the measurement, where the ‘‘collapse of the wavefuction’’ is discontinuous and stochastic. Thus the modern approach tends to remove any postulated theory of measurement...)."

"The point is that standard proofs of ‘‘Bell’s theorem’’ rest upon the theory of measurement (and preparation of states)."

...

A poor reference indeed. You may as well be quoting yourself. Santos is a sad figure (in my personal opinion), whose grand contribution is to convince a few good people that "all loopholes should be closed simultaneously" (a questionable conclusion).

His referenced result is not generally accepted any more than Santos' stochastic mechanics hypotheses, all of which have been soundly critiqued. Gosh, they were published too! You'll have to do a lot better than this.

 

[SpectraCat]

DrChinese, thank you for your time and your letters, I do appreciate them. Actually, they are quite helpful.

Unfortunately, I cannot answer all your questions immediately. I'll try to do it later, but let me start somewhere. So here's the reference:

E. Santos, "Bell’s theorem and the experiments: Increasing empirical support for local realism?", Studies in History and Philosophy of Modern Physics, 36 (2005) 544–565. It's mostly Section 7.

Some quotes:

"According to the traditional formulation, quantum mechanics consists of two quite different ingredients: the formalism (including the equations) and the theory of measurement, both of which are postulated independently. (Actually the two ingredients are to some extent contradictory, because the quantum evolution is continuous and deterministic except during the measurement, where the ‘‘collapse of the wavefuction’’ is discontinuous and stochastic. Thus the modern approach tends to remove any postulated theory of measurement...)."

"The point is that standard proofs of ‘‘Bell’s theorem’’ rest upon the theory of measurement (and preparation of states)."

Santos then mentions other elements of the measurement theory than PP, but you do need PP to calculate the correlations for quantum mechanics: say, you measure a spin projection of one particle of the entangled pair, say, you get value +1, then you use PP to state that after the measurement the system has a definite spin projection of the first particle, then you use UE to state that, due to conservation of angular momentum, the spin projection of the other particle on the same axis is -1, and only then you use the Born rule to find the probability of the other particle having a certain projection of spin on another axis. As the two measurements are spatially separated, it does not matter if you conduct one measurement earlier than the other, later, or simultaneously.

So you cannot take the Malus law from nowhere. It cannot appear in the proof of the Bell's theorem as an experimental law, it can appear there only as a derived result of quantum mechanics, otherwise you cannot say that quantum mechanics predicts nonlocality. And to derive the Malus law in quantum mechanics, you need the theory of measurement, e.g., PP (as I described above).

Ok, so I think I finally understand why it has been to hard to understand your point of view here, at least in my case. You are actually challenging the foundations of the standard formulation of quantum mechanics, by attacking one of the core postulates. This is of course fine, but it would have been helpful if you constructed your arguments in that context from the beginning, rather than focusing on the Bell theorem, which is actually just collateral damage from your primary attack.

In truth, there is nothing wrong with Bell's theorem, because he simply takes for granted the postulates that are part and parcel of SQM ... that is what one is *supposed* to do with postulates, when working within a theoretical framework. On the other hand, you refuse to accept one of those postulates, as you have stated consistently from the beginning, and of course this is the really the only logical grounds on which to challenge an otherwise correct mathematical proof/derivation.

EDIT: As I said above, this is fine, but it is hardly mainstream in this case. While the "measurement problem" has been debated long and hard in quantum mechanics, I think most people would still concede that this has not so far proved to be a practical problem for either measurements, or for theoretical predictions derived from the accepted postulates.

Your challenges on the experimental side of things are also hard for me to accept, but as we have already realized, that is because I tend to accept the fair sampling assumption as valid, while you do not. We have each stated our case, and I guess neither has been convinced by the other ... we will simply have to wait for improved detection efficiencies to resolve this matter I guess.

So, while I tend to view your challenge to SQM as rather quixotic, who is to say that I am correct? All I can say is that the postulates of SQM have served us rather well to this point, and there are no clear-cut cases where they have been found to be false. Perhaps there is a point to be made that they are somehow self-contradictory, but so far that is not a widely held view. I have no problem "rationalizing away" the seeming contradiction that you raise, because the unitary evolution postulate pertains to the microscopic quantum system, whereas the measurement postulate pertains to the interaction of the quantum system with a macroscopic detector. Thus the apparent irreversibility that seems to be the focus of your concerns could in my view just be an "effective irreversibility" resulting from entropic effects as the quantum system interacts with the (effectively) continuous distribution of states represented in the macroscopic detector. I think that if this is correct (and I am not claiming that it is), it would be provide a nice symmetry with classical physics, where temporal irreversibility is also just an "effective" phenomenon resulting from the tendency of natural systems to seek states of high entropy.

 

[DrChinese]

... This is of course fine, but it would have been helpful if you constructed your arguments in that context from the beginning, rather than focusing on the Bell theorem, which is actually just collateral damage from your primary attack.

In truth, there is nothing wrong with Bell's theorem, because he simply takes for granted the postulates that are part and parcel of SQM ... that is what one is *supposed* to do with postulates, when working within a theoretical framework. On the other hand, you refuse to accept one of those postulates, as you have stated consistently from the beginning, and of course this is the really the only logical grounds on which to challenge an otherwise correct mathematical proof/derivation.
...

I don't follow your assessment of the relationship of sQM and Bell. All Bell depends upon is the prediction of sQM - nothing else. It does not assume that prediction is correct. There is nothing about a Bell test, either, that assumes QM is correct. Maybe it isn't.

Either way, the point of Bell was to demonstrate that the Local Realistic view and the QM views are not compatible. After 1935, it was widely believed that they might be.

 

[SpectraCat]

I don't follow your assessment of the relationship of sQM and Bell. All Bell depends upon is the prediction of sQM - nothing else. It does not assume that prediction is correct. There is nothing about a Bell test, either, that assumes QM is correct. Maybe it isn't.

Either way, the point of Bell was to demonstrate that the Local Realistic view and the QM views are not compatible. After 1935, it was widely believed that they might be.

Right, and the prediction of sQM follows from the postulates of sQM, that is all I am saying with the above. If one of those postulates were incorrect, as akhmeteli has hypothesized, then the prediction of sQM could be "wrong", which would then obviously impact the Bell theorem as well. Of course, as I have written, I find akhmeteli's characterization highly suspect ... I accept both the postulates of sQM and the Bell theorem as valid. However at least I now understand where he is coming from ...

 

[MaxwellsDemon]

The postulates were chosen in accordance with experimental observations...basically because they work. Personally I think it would be nice if we could replace the highly abstract and mathematical postulates of QM with postulates that still make the same predictions but are more more physically intuitive aesthetically pleasing...more "human". When studying QM, I always get the feeling that I'm starting with Fermat's Last Theorem as an axiom and trying to prove that 2+2=4.

On a side note, I haven't been on this forum for a while...I'm amazed to see that this thread is still active! I thought the matter seemed settled on the first couple pages last I checked.

Oh, and I thought I'd mentioned that I really like beer. I think it tastes great. Nothing like beer and pizza...or beer and burgers...or beer and ____. :D

"Beer is proof that God loves us and wants us to prosper" - Ben Franklin

 

[DrChinese]

Right, and the prediction of sQM follows from the postulates of sQM, that is all I am saying with the above. If one of those postulates were incorrect, as akhmeteli has hypothesized, then the prediction of sQM could be "wrong", which would then obviously impact the Bell theorem as well. Of course, as I have written, I find akhmeteli's characterization highly suspect ... I accept both the postulates of sQM and the Bell theorem as valid. However at least I now understand where he is coming from ...

So I think we are in sound agreement: Wrong postulates COULD possibly lead to bad predictions; bad predictions would lead to experimental falsification. But regardless, that has NO IMPACT at all on the incompatibility of QM and LR which Bell's Theorem addresses.

Ergo, bad postulates do not invalidate Bell's Theorem. Bell's Theorem in no way says "IF LR is wrong, then QM is true" or vice versa. They could both be false.

 

[DrChinese]

Oh, and I thought I'd mentioned that I really like beer. I think it tastes great. Nothing like beer and pizza...or beer and burgers...or beer and ____. :D

"Beer is proof that God loves us and wants us to prosper" - Ben Franklin

SpectraCat still owes me a couple of beers and refuses to pay up.

 

[Frame Dragger]

So, at what point do you accuse someone of being a crackpot who talks endlessly without producing meanginful citations, of being ATM in the thread; relentlessly and annoyingly? (ahkmeteli)

I realize this is a largely civil forum, but I feel that many pages have been wasted in an interesting discussion so that one indivudual could disagree with SQM without saying so. Can we just move on? DrChinese has stated what I believe all relevant members of this discusson agree on, and we can continue. We don't even need to agree with SQM, or Bells Theorem. Surely nothing could be simpler.

 

[ThomasT]

None of what you are saying makes any sense .. in one breath you say that for entangled particles, the coincidence rate between A & B depends on cos2theta, and in the next breath you say that A & B are "completely random" for any choices of theta besides zero and pi/2. These statements are mutually contradictory.

Let's try again.

At the outset of a run in an idealized, two-photon, optical Bell test the detection rate probabilities are:

for individual detection

P(A) = P(B) = 1/2


and for joint detection

P(A,B) = cos²Θ .


A and B are sets of time-ordered, random-valued, individual detection attributes -- unpredictable sequences of 1's and 0's.

The individual detection rates at A and B aren't correlated to each other, or to Θ, or to λ, or to a or b (the polarizer settings at A and B, respectively). They never vary from 1/2.

However, due to the assumption of common properties imparted to counter-propagating disturbances via emission, then if the value of Θ is known to be 0 or π/2, then if the attribute at A is known then the attribute at B for the pair can be deduced (and vice versa).


The set (A,B) is constructed by pairing the members of A with the members of B wrt detection times. The values of the members of (A,B) also occur randomly.

P(A,B), or the number of pairs containing identical detection attributes is correlated to Θ, and varies as cos²Θ.

Ok so far?

... all of the A & B data sets in all the Bell test experiments ever carried out are "completely random" or "uncorrelated", or whatever you call it. Do you really believe that is true?

Yes. See above.

You still haven't (in fact nobody has) said what you think about the argument against the usual interpretation of the meaning of Bell's theorem and violations of Bell inequalities. I've restated it many times. It has simply to do with the contradiction between the factorability of a Bell LHV joint probability representation and Bell test experimental designs, as well as the contradiction between this factorability and QMs nonfactorable joint (entangled) state representation.

 

[SpectraCat]

Let's try again.

At the outset of a run in an idealized, two-photon, optical Bell test the detection rate probabilities are:

for individual detection

P(A) = P(B) = 1/2

Just to be clear here, in a standard Bell test, *both* polarization components are measured at A and B. So, as long as you are not equating 0 with "no detection event", then I agree with your statement. What the value of 1/2 signifies to me is that, at detector A, a result of "H" is observed half the time, and "V" is observed for the other half of the events; they are never observed simultaneously. Here "H" and "V" refer to two orthogonal polarization directions.

and for joint detection

P(A,B) = cos²Θ .

Again, just to be clear, this is the case for an entangled source only ... the cos²Θ relationship will not hold for unentangled particles. If you use your earlier example of two independent, randomly polarized counter-propagating beams, then for *any* choice of measurement angles at A and B, you will observe P(A,B)=P(A)P(B)=1/4 (that is, paired detection events satisfying any particular choice of "H" and "V" at both A and B will be observed one quarter of the time).

Furthermore, you can make the polarization relationship between the two *independent* beams whatever you like, and while the overall analysis will become more complicated, Alice will still observe that the probability of observing a particular result at A remains independent of the choice of detection settings at B. That is how she can tell whether or not Bob is using an entangled source or not in the thought experiment I have described in my last few posts.

A and B are sets of time-ordered, randomly occurring individual detection attributes -- unpredictable sequences of 1's and 0's.

The individual detection rates at A and B aren't correlated to each other, or to Θ, or to λ, or to a or b (the polarizer settings at A and B, respectively). They never vary from 1/2.

Agreed ... and perhaps my phrasing was somehow unclear, but I never claimed anything different from this. What I have been saying is that for entangled particles, the likelihood of obtaining a coincidence between paired results at A and B depends in a predictable and non-random way on the relative choice of detection angles, which we have been calling Θ. (Note that it is only the relative value of theta that matters ... the absolute settings in the lab frame at A and B are irrelevant.) For unentangled particles, there is no general dependence of the coincidence rate on the choice of Θ, period.

However, due to the assumption of common properties imparted to counter-propagating disturbances via emission, then if the value of Θ is known to be 0 or π/2, then if the attribute at A is known then the attribute at B for the pair can be deduced (and vice versa).

I would phrase this differently. I would say that, in any setup, one can attempt to make a prediction of a measurement result at detector B, based on the observed result at A and the relative detection angle Θ. In the case of entangled particles, one will find upon comparing paired measurements that the chance that their prediction was correct is either cos²Θ, or 1 - cos²Θ, depending on particular type of entanglement. (As you say, these values become 0 and 1 for the choices of Θ you have been focusing on.) In the case of unentangled particles, one would find that the chance of their prediction being correct is independent of the choice of Θ.

But please consider what happens in both of our pictures when we change Θ by an infinitesimal amount from one of these values (0 or π/2). In my case, the chance of the prediction being correct changes by an infinitesimal amount .. in your case the results become "completely random", to use your words.

The set (A,B) is constructed by pairing the members of A with the members of B wrt detection times, and is also a random sequence.

I think the use of "random" is too vague here. I agree that the results of any particular pair cannot be predicted with certainty in the general case, however the likelihood of a coincidence is given by cos²Θ, so it is not purely random either. That is why I choose the term "correlated" ... I would use "perfectly correlated" or "perfectly anti-correlated" to describe the situation at Θ=0 and Θ=π/2.

P(A,B), or the number of pairs containing identical detection attributes is correlated to Θ, and varies as cos²Θ.

Again, I emphasize that P(A,B)=cos²Θ is only obtained for entangled particles. If you are restricting your statement to that case, then I agree.

 

[SpectraCat]

You still haven't (in fact nobody has) said what you think about the argument against the usual interpretation of the meaning of Bell's theorem and violations of Bell inequalities. I've restated it many times. It has simply to do with the contradiction between the factorability of a Bell LHV joint probability representation and Bell test experimental designs, as well as the contradiction between this factorability and QMs nonfactorable joint (entangled) state representation.

Sure I have ... I have said that I thought that such arguments make no sense for the reasons that we have been discussing. The whole Alice and Bob thought experiment I have devised is intended to show that the "inherent contradiction" you mention regarding the experimental design of Bell tests does not exist. (DrChinese has also made similar points.) You have yet to understand the crux of my arguments, but that may be because I have not yet communicated my points clearly ... thus I keep trying.

 

[DrChinese]

1. The individual detection rates at A and B aren't correlated to each other, or to Θ, or to λ, or to a or b (the polarizer settings at A and B, respectively). They never vary from 1/2.

2. However, due to the assumption of common properties imparted to counter-propagating disturbances via emission, then if the value of Θ is known to be 0 or π/2, then if the attribute at A is known then the attribute at B for the pair can be deduced (and vice versa).

1. Not exactly sure what you are saying here. I think you are saying that the values are random no matter where across 360 degrees you place the settings. There IS a correlation for Theta, although the values themselves are still random.

2. I think you are re-stating the QM rule used to get the prediction of cos^2(theta). I guess you could call it an assumption used to make the prediction, but that is really simply saying it is part of the theory (or theory application). It is not an assumption of Bell. It is more part of EPR.

 

[SpectraCat]

SpectraCat still owes me a couple of beers and refuses to pay up.

Heh! I haven't conceded that I actually lost those beers yet ... but I can only carry on so many arguments at one time ... I hope to pick up ours again later.

Still, if ever I make it to Texas, I will look you up and buy you a couple brews, just to keep you quiet!

 

[DrChinese]

Still, if ever I make it to Texas, I will look you up and buy you a couple brews, just to keep you quiet!

That works for me...

 

[Frame Dragger]

Heh! I haven't conceded that I actually lost those beers yet ... but I can only carry on so many arguments at one time ... I hope to pick up ours again later.

Still, if ever I make it to Texas, I will look you up and buy you a couple brews, just to keep you quiet!

Better yet: Oktoberfest in Germany as the location of 'The First National XXVIIth Industrial Summit For The Regulation of Swatches' could be a place to discuss physics in addition to the nature of swatches, and swatch regulation. Perhaps the argument as to wheh a swatch becomes a SAMPLE could be seen as the line between the macroscopic and microscropic in physics? Maybe I haven't slept in over 36 hours and my brain is playing tricks on me? *plays kazoo; runs away*

 

[ThomasT]

Just to be clear here, in a standard Bell test, *both* polarization components are measured at A and B. So, as long as you are not equating 0 with "no detection event", then I agree with your statement. What the value of 1/2 signifies to me is that, at detector A, a result of "H" is observed half the time, and "V" is observed for the other half of the events; they are never observed simultaneously. Here "H" and "V" refer to two orthogonal polarization directions.

In the tests (eg. Aspect '82) I was thinking of, the counter-propagating optical disturbances incident on the polarizers are assumed to have identical polarizations. A detection attribute of "0" means no detection. The probability 1/2 means that the rate of detection at A and B with polarizers in place is 1/2 the rate of detection at A and B without polarizers. (And, since we're considering an idealization, the value 1/2 means that for N counter-propagating pairs emitted it's expected that N/2 detections will be registered at A and N/2 detections at B.)

... the cos2Θ relationship will not hold for unentangled particles.

It might. For example, consider the standard (a la Aspect) Bell test setup, then add a polarizer between the emitter and the polarizer on each side. Let the transmission axes of these two additional polarizers be always aligned and changing randomly. Now the counter-propagating disturbances transmitted by the first set of polarizers are identically polarized, but not entangled. Then the resulting angular dependency will still be cos2Θ, but the probability or normalized rate of joint detection will be .125(1-(2cos2Θ).

What I have been saying is that for entangled particles, the likelihood of obtaining a coincidence between paired results at A and B depends in a predictable and non-random way on the relative choice of detection angles, which we have been calling Θ.

I guess we're on the same page then.

... due to the assumption of common properties imparted to counter-propagating disturbances via emission, then if the value of Θ is known to be 0 or π/2, then if the attribute at A is known then the attribute at B for the pair can be deduced (and vice versa).

I would phrase this differently. I would say that, in any setup, one can attempt to make a prediction of a measurement result at detector B, based on the observed result at A and the relative detection angle Θ. In the case of entangled particles, one will find upon comparing paired measurements that the chance that their prediction was correct is either cos2Θ, or 1 - cos2Θ, depending on particular type of entanglement. (As you say, these values become 0 and 1 for the choices of Θ you have been focusing on.) In the case of unentangled particles, one would find that the chance of their prediction being correct is independent of the choice of Θ.

But please consider what happens in both of our pictures when we change Θ by an infinitesimal amount from one of these values (0 or π/2). In my case, the chance of the prediction being correct changes by an infinitesimal amount .. in your case the results become "completely random", to use your words.

I think my phrasing is pretty clear (and yours is somewhat confusing). Keep in mind that we're considering idealization of Bell test. What can be deduced about B given knowledge of A and Θ?

I have said that I thought that such arguments make no sense for the reasons that we have been discussing. The whole Alice and Bob thought experiment I have devised is intended to show that the "inherent contradiction" you mention regarding the experimental design of Bell tests does not exist.

Let's try again. I'll ask some questions beginning with:

Do you understand that P(A,B) = P(A)P(B), the definition of statistical independence, is also the definition of Bell locality?

 

[akhmeteli]

A poor reference indeed. You may as well be quoting yourself.

Whether it's poor or not, it serves its purpose. Indeed, why did I need this reference in the first place? Not to convince you, but to prove that I complied with the forum rules and did not push any personal theory.

Now let us ask ourselves what is exactly controversial in the Santos' quotes I offered? The first quote about the contradiction between the equations of QM and the theory of measurement of QM? But we don't need to believe Santos, as I offered other references confirming this. Furthermore, you yourself "freely admit" the measurement problem in QM. So I just don't quite see what's controversial about the first quote.

Second quote? It says that "standard proofs of ‘‘Bell’s theorem’’ rest upon the theory of measurement". But can we really say with a straight face that we can get the expression for the correlations in QM without the theory of measurement of QM? I don't think so. If you do, then how exactly can you get this expression? You cannot get it from UE, because it is very difficult to compute UE for the particles plus the measuring instruments. Nobody does that to prove Bell. And there is nothing in QM but UE and the theory of measurement. And, as I said, you cannot just use the Malus law until you prove it based exclusively on the postulates of QM (otherwise the correlations will not be based on QM, so it will not be proven that the Bell inequalities can be violated in QM). Furthermore, you cannot use the theory of measurement to prove the Malus law, otherwise the second Santos' quote will still stand.

Santos is a sad figure (in my personal opinion), whose grand contribution is to convince a few good people that "all loopholes should be closed simultaneously" (a questionable conclusion).

Then let me ask you again (I don't remember which time it is - my understanding is I have not heard your opinion on this point), what's exactly wrong with my Euclidean geometry "proof", if it's "questionable" that ALL assumptions of a theorem must be fulfilled simultaneously to ensure its conclusion stands?

His referenced result is not generally accepted any more than Santos' stochastic mechanics hypotheses, all of which have been soundly critiqued. Gosh, they were published too! You'll have to do a lot better than this.

I have proven with this reference that I did not offer any personal theory. Could you please indicate which Santos' quote you personally disagree? The first? The second? Both? Again, I offered other references confirming the first quote and I offered some arguments (in this and the previous posts) confirming the second one.

 

[Frame Dragger]

Whether it's poor or not, it serves its purpose. Indeed, why did I need this reference in the first place? Not to convince you, but to prove that I complied with the forum rules and did not push any personal theory.

You cite sources because:
1.) you claim to have them
2.) Why should anyone care about a baseless opinion in THIS forum (try general)
3.) The rules are the rules.

Your "source" serves no purpose; it only goes to the argument that you're just filling pages with your baseless sophistry, now girded by the baseless sophistry of one other person. You constantly attempt to pivot on the question and keep the rhetoric going, but this is not the point of a PHYSICS forum. Cite a meanginful source, answer the questions you've been asked, or take DrChinese's advice and leave the thread if not physics as a whole.

EDIT: Using Santos, who has no personal or professional crediblity or gravitas, is as close as you come in rhetoric to using a real straw man. A real man, if not really made of straw . As Santos is not respectable, and you have freely aditted the "utility" of your citation the issue returns to your personal beleifs.

 

[SpectraCat]

In the tests (eg. Aspect '82) I was thinking of, the counter-propagating optical disturbances incident on the polarizers are assumed to have identical polarizations. A detection attribute of "0" means no detection. The probability 1/2 means that the rate of detection at A and B with polarizers in place is 1/2 the rate of detection at A and B without polarizers. (And, since we're considering an idealization, the value 1/2 means that for N counter-propagating pairs emitted it's expected that N/2 detections will be registered at A and N/2 detections at B.)

Aspect '82, while groundbreaking, is not up to date ... you no longer need to discard half the samples, as I pointed out in my post.

It might. For example, consider the standard (a la Aspect) Bell test setup, then add a polarizer between the emitter and the polarizer on each side. Let the transmission axes of these two additional polarizers be always aligned and changing randomly. Now the counter-propagating disturbances transmitted by the first set of polarizers are identically polarized, but not entangled. Then the resulting angular dependency will still be cos2Θ, but the probability or normalized rate of joint detection will be .125(1-(2cos2Θ).

I don't understand this yet ... I will think about it some more and respond. I am pretty sure that this case should be distinguishable from true entanglement, but I don't quite see how (yet).

I guess we're on the same page then.

Great!

I think my phrasing is pretty clear (and yours is somewhat confusing). Keep in mind that we're considering idealization of Bell test. What can be deduced about B given knowledge of A and Θ?

The probability of observing a coincident detection event within the experimental definition of such an event, as I have said.

Let's try again. I'll ask some questions beginning with:

Do you understand that P(A,B) = P(A)P(B), the definition of statistical independence, is also the definition of Bell locality?

I certainly agree that it is part of the definition ...

 

[zonde]

Again, just to be clear, this is the case for an entangled source only ... the cos²Θ relationship will not hold for unentangled particles. If you use your earlier example of two independent, randomly polarized counter-propagating beams, then for *any* choice of measurement angles at A and B, you will observe P(A,B)=P(A)P(B)=1/4 (that is, paired detection events satisfying any particular choice of "H" and "V" at both A and B will be observed one quarter of the time).

It might be interesting to note that as it seems the same source that is used for generation of entangled pairs can be used to generate completely factorizable state i.e. P(A,B)=P(A_H)P(B_H)+P(A_V)P(B_V) that can be described using polarizator angles of Alice and Bob but can not be described using only relative angle.

 

[Demystifier]

You see, I can live with nonlocality, no problem at all. I'm just curious: why should I?

Because there are many proofs that the world is nonlocal, even though none of these proofs is the Proof. (I hope you understand what I mean. If you don't, despite all the efforts of me and other contributors here, then I cannot find any new way to explain it to you.)

... no experimental demonstration of violations of the genuine Bell inequalities.

But we do have experimental demonstration of what-you-would-call non-genuine Bell inequalities. These experimental results are easily explained by nonlocal QM (combined with some approximations, of course), but are very difficult to explain with local laws of physics. Perhaps not impossible, but very difficult.

So we are left with no-go theorems, such as the Bell theorem. But if it uses approximations as assumptions, that opens a hole for locality. Is this hole wide enough or too narrow? I don't know. Do you?

I think it is the crucial question: Is this hole wide enough or too narrow? We do not have an exact measure of the wideness of this hole, but most physicists agree, even some of those you cited as a support of your views, that the hole seems rather narrow. So, if you ask me to estimate the likelyhoods that nature is nonlocal or local, my subjective estimate would be something like 99:1. What would be yours?

You were very kind to call one of my ideas "interesting", and I am grateful to you, but that idea was based on a rigorous result. Actually, we all do what we can, not what we want.

With that I agree. But that idea cannot be applied to the real world without some approximations that make it non-rigorous. Which, for me, does not make your idea less interesting.

 

[Eye_in_the_Sky]

It looks like my opportunity to post at the forum is about to end. I feel hard-pressed, though, to (at least attempt to) close off as much as possible of what I have opened up.

Many posts ago, the first part of Bell's argument (in Bell's original paper) was summarized as follows:

Proposition 1: locality Λ PC Λ CF → local determinism ,

where

CF ≡ counterfactuality

and

PC ≡ perfect anti-correlation for equal settings .

The idea is that the above proposition can be joined to the second part of Bell's argument (in Bell's original paper) which can be summarized as:

Proposition 2: local determinism → D ,

where "D" is a certain condition (which turns out to be inconsistent with Quantum Mechanics).

So, there are two 'theorems', a weak one and a strong one:

Weak Theorem: local determinism → D ;

Strong Theorem: locality Λ PC Λ CF → D .
___________________

Let's say I too see this proposition as valid but not exhaustive ...

Zonde, it has been quite a while. ... But I see you are still around.

... (I would feel more comfortable if I somehow could make sure that all the abstract terms in this proposition have unambiguous meaning).

I see two distinct 'levels' at which one can work in order to establish the validity of "Proposition 1".

One of these levels, I call the "object-level". At the object-level, one analyzes the scenario in terms of outcomes and potential outcomes as they may (or may not) occur in the given physical situation.

However, at this level, the argument suffers from ambiguity due to a lack of clarity in the definition of its essential terms. Just look at the definitions of "locality" and "CF" which one has to work with. These definitions are expressed in terms of words of informal, ordinary language.

For "locality", we have Einstein's words:

The real factual situation of the system S₂ is independent of what is done with the system S₁, which is spatially separated from the former.

And what about "CF"? At the object-level, "CF" becomes none other than "CFD", that is, "counterfactual definiteness", which as Stapp (the conceiver of the notion) explains is:

For each particle on which a measurement is performed, a definite value would have been found if a different spin component had been measured on it instead (although we cannot know what the specific value would have been) and, furthermore, the complete set of such values (measured and unmeasured together) can be meaningfully discussed.

But there is another level at which one can work to establish the validity of "Proposition 1". I call it the "meta-level". Here, one analyzes the scenario in terms of the joint-probability-function as it would be calculated at the level of a physical theory. At this level, "locality" can be defined in unambiguous, mathematical terms (i.e. in terms of "Bell Locality", which I took a step towards defining back in post #239 (but I have not yet followed up on it)), while "CF" turns out to correspond to "the permissibility of exploring the causal structure of a physical theory".
___________________

I would say that PC is not a requirement for local determinism. So we can say: locality Λ CF → local determinism.

"Locality Λ CF" alone is not enough. As far as I can tell, "PC" is essential to the argument, in which case there is not even a substitute for it.

That's because PC is certain arrangement of things that applies to one situation but doesn't apply to other.

I can't tell what you're getting at here.
___________________

What I don't like about this theorem of QM is that it is placed as restriction on all possible LR theories even when this theorem is not experimentally verified.

Zonde ... you are starting to lose me. I would think that "PC" ought to be a feature of any theory. Is "PC" not just the expression of conservation of angular momentum for a system whose angular momentum was initially zero?

Let's say we can formulate LR theory that says:
a) If measurement of the component σ1∙a, where a is some unit vector, yields the value +1, then measurement of σ2∙a must yield the value -1 or no value at all at least half the time.
b) If measurement of the component σ1∙a, where a is some unit vector, yields the value +1, then low efficiency measurement of σ2∙a must yield the value -1 with very high probability and value +1 with very low probability or no value at all. But as measurement efficiency increases relative probability of +1 value increases rapidly.

Okay. ... Now I'm lost.

 

[Eye_in_the_Sky]

1) Do you believe you understand the concept expressed by the following statement?

Alice and Bob's outcomes are governed by local determinism.

2) Do you consider the following statement to be true?

On the basis of the single assumption of "local determinism of Alice and Bob's outcomes", one can derive a Bell inequality.

I think so

I think so

How about this next statement, would you say that it is correct?

The assumption of "local determinism of Alice and Bob's outcomes" is independent of any assumptions concerning the truth or internal consistency of Quantum Mechanics.

I think I disagree with this statement. Indeed, if QM is true and internally consistent, then the Bell inequalities can indeed be violated, so local determinism is eliminated. Therefore the assumption of local determinism does not seem to be independent of the assumptions of truth and consistency of quantum mechanics.

Thank you, akhmeteli, for answering my questions. Originally, it appeared to me that there may have been some misconception in the way you were thinking about Bell's Theorem. But from the answers you have given, I do not detect any such misconception.

Indeed, we both agree:

local determinism → D

and

QM → ~D ,

where D is a certain condition.


So finally I am able to understand your position. Essentially, you are saying that the QM prediction of "~D" might be WRONG, and if so, then Bell's Theorem is of LITTLE significance.

But I think that even if this QM prediction did turn out to be wrong, Bell's Theorem would nonetheless be HIGHLY significant. It would still be telling us that two of THE MOST MAJOR world-views EVER to be found in the HISTORY of SCIENCE are FUNDAMENTALLY INCOMPATIBLE.

[The only remaining question (for me, at least) is whether or not one can derive the condition "D" from premises which are logically weaker than the premise of "local determinism" ... thereby strengthening Bell's Theorem.]

 

[Dmitry67]

Hm
Imagine that QM is not discovered yet (but SR is discovered)
However, there are many EPR Alice/Bob experiments and tons of data
I was thinking that in that case it would be possible to rule out local theories, even without QM, just based on the experiments. AM I wrong?

 

[Frame Dragger]

Hm
Imagine that QM is not discovered yet (but SR is discovered)
However, there are many EPR Alice/Bob experiments and tons of data
I was thinking that in that case it would be possible to rule out local theories, even without QM, just based on the experiments. AM I wrong?

Maybe... but you'd be creating QM based on the predictions you'd expect a given non-local theory to match. People would probably laugh you out of the room in the absence of QM too. Logically I see your point, but practically, not so much.

 

[zonde]

One of these levels, I call the "object-level". At the object-level, one analyzes the scenario in terms of outcomes and potential outcomes as they may (or may not) occur in the given physical situation.

However, at this level, the argument suffers from ambiguity due to a lack of clarity in the definition of its essential terms. Just look at the definitions of "locality" and "CF" which one has to work with. These definitions are expressed in terms of words of informal, ordinary language.

For "locality", we have Einstein's words:

The real factual situation of the system S₂ is independent of what is done with the system S₁, which is spatially separated from the former.

Ambiguity in this definition is that experiments are done with ensembles. SQM formalism refers to ensembles too. But in discussions single photons are used instead of ensembles.
So what leaves a doubt is if photons from ensemble at different times occupy the same place should this be treated as "locality" or not. But this is quite specific so I think it shouldn't cause problems in most cases.

And what about "CF"? At the object-level, "CF" becomes none other than "CFD", that is, "counterfactual definiteness", which as Stapp (the conceiver of the notion) explains is:

For each particle on which a measurement is performed, a definite value would have been found if a different spin component had been measured on it instead (although we cannot know what the specific value would have been) and, furthermore, the complete set of such values (measured and unmeasured together) can be meaningfully discussed.

That's clear. But does it mean that deterministic chaos is completely excluded by this definition?
It's hard to accept that deterministic chaos somehow contradicts local realism.

"Locality Λ CF" alone is not enough. As far as I can tell, "PC" is essential to the argument, in which case there is not even a substitute for it.I can't tell what you're getting at here.

Zonde ... you are starting to lose me. I would think that "PC" ought to be a feature of any theory. Is "PC" not just the expression of conservation of angular momentum for a system whose angular momentum was initially zero?

"PC" is essential for Bell's argument but is it essential for local realism?
And how you define "PC"?
Say if light is linearly polarized and then it goes through polarizer with the same orientation of polarization axis as for light. All light is passing through polarizer - perfect measurement.
Now polarizator is oriented at different angle and measurement becomes probabilistic.
Are you saying that local realism requires that probability for individual photon can depend only from properties of photon and in no way from context?

Now if we have chaotic context that determines probability and say we include some controllable factor that contributes to context. Now the the outcome will become predictable but only marginally. We can not eliminate chaotic context we can only override it with controllable factors to some extent.
Therefore I say "PC" are not realistic.

 

[zonde]

But we do have experimental demonstration of what-you-would-call non-genuine Bell inequalities. These experimental results are easily explained by nonlocal QM (combined with some approximations, of course), but are very difficult to explain with local laws of physics. Perhaps not impossible, but very difficult.

This is no surprise that facts can be more easily explained using less restrictive rules than more restrictive rules.
Well if we talk about that I can explain anything using one rule - God wished it to be so. Are you satisfied with that explanation?

 

[Frame Dragger]

This is no surprise that facts can be more easily explained using less restrictive rules than more restrictive rules.
Well if we talk about that I can explain anything using one rule - God wished it to be so. Are you satisfied with that explanation?

Why did you respond to a valid point with the ultimate in reductio ad absurdem?

 

[DrChinese]

Whether it's poor or not, it serves its purpose. Indeed, why did I need this reference in the first place? Not to convince you, but to prove that I complied with the forum rules and did not push any personal theory.

Now let us ask ourselves what is exactly controversial in the Santos' quotes I offered? The first quote about the contradiction between the equations of QM and the theory of measurement of QM? But we don't need to believe Santos, as I offered other references confirming this. Furthermore, you yourself "freely admit" the measurement problem in QM. So I just don't quite see what's controversial about the first quote.

Second quote? It says that "standard proofs of ‘‘Bell’s theorem’’ rest upon the theory of measurement". But can we really say with a straight face that we can get the expression for the correlations in QM without the theory of measurement of QM? I don't think so.

All references are not equal, so please, you know better. Santos has been soundly plastered in his defence of LHV theories.

There is a measurement problem in QM, but it is not the kind of problem you imply. It is more of a theory scope issue. And it has nothing to do with Bell. As previously mentioned ad nauseum, if QM is wrong... so be it. But that does not change the fact that QM and LR are incompatible, which is the Bell result.

If you don't understand that QM IS CAPABLE of making predictions, then you haven't heard anything everyone has been telling you. I don't care what Santos said, he has a major ax to grind and wants to discredit any aspect of Bell, Bell tests, QM, etc. it takes in order to convince everyone he is "right" whatever that means. So far, he has been wrong about every single Bell experiment, has made zero correct predictions, and has added zero to our understanding of entanglement - a state he denies exists.

 

[akhmeteli]

Ok, so I think I finally understand why it has been to hard to understand your point of view here, at least in my case. You are actually challenging the foundations of the standard formulation of quantum mechanics, by attacking one of the core postulates. This is of course fine, but it would have been helpful if you constructed your arguments in that context from the beginning, rather than focusing on the Bell theorem, which is actually just collateral damage from your primary attack.

In truth, there is nothing wrong with Bell's theorem, because he simply takes for granted the postulates that are part and parcel of SQM ... that is what one is *supposed* to do with postulates, when working within a theoretical framework. On the other hand, you refuse to accept one of those postulates, as you have stated consistently from the beginning, and of course this is the really the only logical grounds on which to challenge an otherwise correct mathematical proof/derivation.

EDIT: As I said above, this is fine, but it is hardly mainstream in this case. While the "measurement problem" has been debated long and hard in quantum mechanics, I think most people would still concede that this has not so far proved to be a practical problem for either measurements, or for theoretical predictions derived from the accepted postulates.

Your challenges on the experimental side of things are also hard for me to accept, but as we have already realized, that is because I tend to accept the fair sampling assumption as valid, while you do not. We have each stated our case, and I guess neither has been convinced by the other ... we will simply have to wait for improved detection efficiencies to resolve this matter I guess.

So, while I tend to view your challenge to SQM as rather quixotic, who is to say that I am correct? All I can say is that the postulates of SQM have served us rather well to this point, and there are no clear-cut cases where they have been found to be false. Perhaps there is a point to be made that they are somehow self-contradictory, but so far that is not a widely held view. I have no problem "rationalizing away" the seeming contradiction that you raise, because the unitary evolution postulate pertains to the microscopic quantum system, whereas the measurement postulate pertains to the interaction of the quantum system with a macroscopic detector.

SpectraCat,

Thank you very much for a fair summary. While you disagree with me, it looks like you don't find this thread a waste of time anymore, and I am happy about that.

Unfortunately, I don't have time to reply to your specific comments right now. I'll try to do that later.

 

[akhmeteli]

Thank you, akhmeteli, for answering my questions. Originally, it appeared to me that there may have been some misconception in the way you were thinking about Bell's Theorem. But from the answers you have given, I do not detect any such misconception.

Indeed, we both agree:

local determinism → D

and

QM → ~D ,

where D is a certain condition.


So finally I am able to understand your position. Essentially, you are saying that the QM prediction of "~D" might be WRONG, and if so, then Bell's Theorem is of LITTLE significance.

But I think that even if this QM prediction did turn out to be wrong, Bell's Theorem would nonetheless be HIGHLY significant. It would still be telling us that two of THE MOST MAJOR world-views EVER to be found in the HISTORY of SCIENCE are FUNDAMENTALLY INCOMPATIBLE.

[The only remaining question (for me, at least) is whether or not one can derive the condition "D" from premises which are logically weaker than the premise of "local determinism" ... thereby strengthening Bell's Theorem.]

Eye_in_the_Sky,

Thank you very much. I am happy that you understood my position.

And I fully agree that the Bell theorem is highly significant no matter what. It pushes standard quantum mechanics to the extreme (and I'd like to emphasize that what you wrote relates to standard quantum mechanics), and this is a great way to test a theory.

 

[akhmeteli]

Because there are many proofs that the world is nonlocal, even though none of these proofs is the Proof. (I hope you understand what I mean. If you don't, despite all the efforts of me and other contributors here, then I cannot find any new way to explain it to you.)

I think I understand what you mean. But then I may say that there are many proofs (rather than Proof) that the world is local, such as: the absence of signal nonlocality; microcausality in quantum field theory; the absence of experimental violations of the genuine Bell inequalities; holes in no-go theorems, and so on.

But we do have experimental demonstration of what-you-would-call non-genuine Bell inequalities. These experimental results are easily explained by nonlocal QM (combined with some approximations, of course), but are very difficult to explain with local laws of physics. Perhaps not impossible, but very difficult.

Fair enough. However, I mentioned the astonishing mathematical trick (published by other people) that makes nonlinear differential equations in 3+1 dimensions look like linear unitary evolution equations of quantum field theory in the Fock space. This mechanism suggests that the explanation may be easier than it seems. I'll try to e-mail you about a specific implementation of this mechanism

I think it is the crucial question: Is this hole wide enough or too narrow? We do not have an exact measure of the wideness of this hole, but most physicists agree, even some of those you cited as a support of your views, that the hole seems rather narrow. So, if you ask me to estimate the likelyhoods that nature is nonlocal or local, my subjective estimate would be something like 99:1. What would be yours?

I cited those physicists just to support my view that LR has not been ruled out yet (I know that Shimony, Zeilinger, Genovese don't believe in LR at all, but that is why their honest assessment of the experimental situation is especially valuable), and, judging by your "subjective estimate", you agree that it has not, although you find LR highly unlikely.

As for my "subjective estimate", you see, on the one hand, I only have scientific basis to state that LR has not been ruled out, and I don't want to start a flame, but now that you ask, I admit that my "subjective estimate" is the inverse of yours. Again, I readily admit that I cannot support this estimate, so it's purely subjective. I fully agree that "We do not have an exact measure of the wideness of this hole". Furthermore, my estimate can change drastically in the future to reflect new experimental and theoretical developments.

With that I agree. But that idea cannot be applied to the real world without some approximations that make it non-rigorous. Which, for me, does not make your idea less interesting.

Thank you very much. But you can be sure that, emphasizing the value of rigorous results, I had no intention to "offend" approximate approaches - of course, physics is impossible without them.

 

[Dmitry67]

It leads me to another question.

Say, we found a mapping of our physical spacetime P and any system in it into some other (abstract) space A. There is 1:1 relationship between P and A.

If theory is nonlocal in P but local in A, would you call such theory local or not?

Example: We map surface into line, R2 into R1
Theory, which is local in R2 is non local in R1.