Can grandpa understand the Bell's Theorem?

[miosim]

No, it most certainly is not predicted by Malus' law which is not about multiple photons (or light beams) measured by separate polarizers, but rather about a single light beam going through two polarizers in succession (or a single pre-polarized beam going through a single polarizer) as I already explained ...

There two differences between Aspect and Malus experiments. First difference is in intensity of light (light beam vs. individual photons). The second difference is that Aspect measures two “perfectly” correlated photons that mirror each other, but the result of this experiment should be the same (cos^2 correlation) as Malus’ experiments with one polarizer for consecutive polarized photons.

It is why the result of Aspect’s experiment is fully predictable from Malus law.

Big surprise, you've been "convinced" of the ignorant opinion you've kept repeating from the very beginning, even though others have already told you, over and over again, that this is complete nonsense (Bell's argument does not assume anything specific about the nature of particles, including whether they behave deterministically, it only uses the basic premises of local realism which I outlined here).

From BELL’S THEOREM : THE NAIVE VIEW OF AN EXPERIMENTALIST (page 13)

“…The second considered hypothesis is determinism. As a matter of fact, the
formalism of section 3.1 is deterministic: once λ is fixed, the results A(λ,a) and B(λ,b) of the polarization measurements are certain.”

Please let me know if you have more questions.

…You continually ignore all the explanations and questions people put to you (like my repeated question about whether you understand why local realism implies that there are predetermined results for each measurement axis)…

I do understand “your local realism” that implies that there are predetermined results for each measurement. Now, do you understand why this deterministic (predetermined results) model is in the “spirit of Einstein’s ideas? I don’t.

…so it kind of seems like you think you already know everything important about Bell's theorem and have no interest in actually learning anything about it from your dialogue here. )…

Now I belief that I understand the most important about Bell's theorem, mostly by carefully reading Bell’s and Aspect’s original papers. At the same time I don’t think I can learn from you as long as you provide the explanation similar to one you gave for local realism in your post #55 (as shown below).

1. The complete set of physical facts about any region of spacetime can be broken down into a set of local facts about the value of variables at each point in that regions (like the value of the electric and magnetic field vectors at each point in classical electromagnetism)

2. The local facts about any given point P in spacetime are only causally influenced by facts about points in the past light cone of P, meaning if you already know the complete information about all points in some spacelike cross-section of the past light cone, additional knowledge about points at a spacelike separation from P cannot alter your prediction about what happens at P itself (your prediction may be a probabilistic one if the laws of physics are non-deterministic)

And I have no choice but ignore these explanations, partially because of your unfriendly mentoring attitudes.

 

[JesseM]

There two minor differences between Aspect and Malus experiments. First difference is in intensity of light (light beam vs. individual photons). The second difference is that Aspect measures both “perfectly” correlated photons that mirror each other, but the result of this experiment should produce the same result (cos^2 correlation) as Malus’ experiments with one polarizer for consecutive polarized photons.

It is why the result of Aspect’s experiment is fully predictable from Malus law.

No, it would be impossible to produce the same correlations in classical electromagnetism. Specifically, imagine a situation where you send two electromagnetic waves in different directions from a common source (prepared in whatever manner you like, for example, you could initially send both through local polarizers that would give them the same polarization angle), then two experimenters at different locations measure them using a polarizer that is set to a random angle on each trial, along with a device which is programmed to give a binary + or - result depending in some way (anyway you like) on the result of the polarizer experiment (for example, the device might be programmed to give + if the intensity is reduced by more than 50%, - if the intensity is reduced by less than 50%. Another possible rule would be that if the reduction in intensity is by a fraction F, the device has a probability F of giving + and a probability 1-F of giving -. But you don't have to use either of those rules, the device can be programmed any way you like as long as it always gives one of two binary results). If there is a spacelike separation between the two measurements, then there is no possible way that this purely classical experiment could give the same result as in QM, namely that that if experimenter #1 sets his polarizer to angle a, and experimenter #2 sets her polarizer to angle b, then the probability that they will both get the same result (both + or both -) is cos^2 (a-b). This despite the fact that Malus' law is still quite operative in this scenario, so for example if the source emitted two beams polarized at angle c and with the same intensity I, experimenter #1 would see the intensity reduced to I*cos^2 (a-c) while experimenter #2 would see the intensity reduced to I*cos^2 (b-c).

If you think there is some way that a purely classical experiment of this type could give the same correlations as predicted by QM in Bell's experiment please give the details, if not you have no excuse to repeat the false claim that the correlations predicted by QM can be derived from the classical Malus' law.

Big surprise, you've been "convinced" of the ignorant opinion you've kept repeating from the very beginning, even though others have already told you, over and over again, that this is complete nonsense (Bell's argument does not assume anything specific about the nature of particles, including whether they behave deterministically, it only uses the basic premises of local realism which I outlined here).

From BELL’S THEOREM : THE NAIVE VIEW OF AN EXPERIMENTALIST (page 13)

“…The second considered hypothesis is determinism. As a matter of fact, the
formalism of section 3.1 is deterministic: once λ is fixed, the results A(λ,a) and B(λ,b) of the polarization measurements are certain.”

Please let me know if you have more questions.

The snide final line suggests again that you have no interest in learning anything, and think you know everything already. But why are you quoting from Aspect's paper when my statement was about Bell's argument? Aspect was using a simplified and less rigorous version of Bell's proof, Bell's more general later proofs talked about the probabilities of getting a result A with setting a, just look at the Bertlmann's socks paper you directed us to earlier, where you can plainly see on p. 15 that he uses probabilistic expressions like P(A|a,λ) and P(B|b,λ), not simple functions like A(λ,a) which assume from the outset that there is only one possible value for A given the values of λ and a.

A subtlety here is that if you start with the basic assumptions of local realism I mentioned earlier:

1. The complete set of physical facts about any region of spacetime can be broken down into a set of local facts about the value of variables at each point in that regions (like the value of the electric and magnetic field vectors at each point in classical electromagnetism)

2. The local facts about any given point P in spacetime are only causally influenced by facts about points in the past light cone of P, meaning if you already know the complete information about all points in some spacelike cross-section of the past light cone, additional knowledge about points at a spacelike separation from P cannot alter your prediction about what happens at P itself (your prediction may be a probabilistic one if the laws of physics are non-deterministic).

Then even though these assumptions say nothing about whether the basic laws are determistic or probabilistic, it is possible to derive from these assumptions the conclusion that if there are perfect correlations whenever the experimenters randomly choose the same detector setting (and their choices are made at a spacelike separation), then the only way to explain this in a way consistent with 1) and 2) is to assume the variables associated with the particles already predetermined their results for all possible measurement settings at some time before the settings were chosen. If you change your mind and decide you're interested in learning something new, I can explain how this conclusion follows from the basic assumptions 1) and 2). But the fact that this conclusion does follow in a natural way from the basic premises of local realism means if you're not interested in full rigor it's OK as a shortcut to simply assume predetermined results from the outset (as Aspect did in his paper), rather than use conditional probabilities as Bell did in the Bertlmann's socks paper.

At the same time I don’t think I can learn from you as long as you provide the explanation similar to one you gave for local realism in your post #55.

1. The complete set of physical facts about any region of spacetime can be broken down into a set of local facts about the value of variables at each point in that regions (like the value of the electric and magnetic field vectors at each point in classical electromagnetism)

2. The local facts about any given point P in spacetime are only causally influenced by facts about points in the past light cone of P, meaning if you already know the complete information about all points in some spacelike cross-section of the past light cone, additional knowledge about points at a spacelike separation from P cannot alter your prediction about what happens at P itself (your prediction may be a probabilistic one if the laws of physics are non-deterministic).

And I have no choice but ignore these explanations, partially because of your unfriendly mentoring attitudes.

Why do you have "no choice" but to ignore my explanations? I didn't become unfriendly until you continually repeated the same statements over and over again, ignoring my repeated explanations as to why they were mistaken. Anyway you're a big boy, I'm sure if you actually had any interest in learning you could learn something from a slightly hostile person. If you just doubt that my assumptions are equivalent to Bell's but are willing to be proven wrong, I already recommended that you try looking at the La nouvelle cuisine paper I linked to and discussed in [post=3248153]this post[/post], if you read it you can see that Bell clearly does use the same assumptions as I do above--my talk of "local facts" in 1) is equivalent to his discussion in section 6.3 here of "local beables" (a "be"able is meant to express an objective fact about what exists, in contrast to QM "observables"), and then section 6.7 here, along with the diagram 6.3 at the top of the page (and diagram 6.4 on the next page), makes it clear that he is defining locality in terms of the idea that the values of local beables in a given region of spacetime can only be causally influenced by events in the past light cone of that region, same as my 2).

If you take the time to look over this paper and still disagree that Bell's assumptions are equivalent to mine, feel free to point out specifically where you think he introduces some additional assumption, but if you just continue to spout the same tired old false claims about Bell's assumptions (and about Malus' law) without giving any sort of specific and substantive response to my corrections, as I said I'll just be reporting your posts to the mods.

 

[miosim]

JesseM,

Let me think about your responds. I am slow.

Thank you,
Mark

 

[miosim]

I would like to clarify my position regarding Malus’ law before discussing the next issues you raised in the previous post.

No, it would be impossible to produce the same correlations in classical electromagnetism. Specifically, imagine a situation where you send two electromagnetic waves in different directions from a common source (prepared in whatever manner you like, for example, you could initially send both through local polarizers that would give them the same polarization angle), then two experimenters at different locations measure them using a polarizer that is set to a random angle on each trial, along with a device which is programmed to give a binary + or - result depending in some way (anyway you like) on the result of the polarizer experiment (for example, the device might be programmed to give + if the intensity is reduced by more than 50%, - if the intensity is reduced by less than 50%. Another possible rule would be that if the reduction in intensity is by a fraction F, the device has a probability F of giving + and a probability 1-F of giving -. But you don't have to use either of those rules, the device can be programmed any way you like as long as it always gives one of two binary results). If there is a spacelike separation between the two measurements, then there is no possible way that this purely classical experiment could give the same result as in QM, namely that that if experimenter #1 sets his polarizer to angle a, and experimenter #2 sets her polarizer to angle b, then the probability that they will both get the same result (both + or both -) is cos^2 (a-b). This despite the fact that Malus' law is still quite operative in this scenario, so for example if the source emitted two beams polarized at angle c and with the same intensity I, experimenter #1 would see the intensity reduced to I*cos^2 (a-c) while experimenter #2 would see the intensity reduced to I*cos^2 (b-c)..

I think that a much simpler approach could be taken to compare the result of Malus law with Bell’s theorem.
The main goal of Bell’s theorem is to demonstrate a difference between the prediction of QM and “local realism” (the way Bell understood it).
The QM model predicts cos^2 (a-b) correlation while the “local realism” yields a linear (saw-like) function. To prove that the QM model is correct, Bell could justify that his theoretical setup is equivalent to Malus’ experimental setup in which both polarizers are placed on the same side of the light source (so the photons need to pass both polarizers in order to reach the target). In this case, the intensity of light that reaches the target is cos^2 (a-b), which proves the correctness of the QM model.

 

[JesseM]

The QM model predicts cos^2 (a-b) correlation while the “local realism” yields a linear (saw-like) function.

I don't think "local realism" yields any specific function, I think the saw-like function is just meant to represent the closest you can come to the cos^2 function in local realism, as I explained in [post=3240160]post #20[/post].

To prove that the QM model is correct, Bell could justify that his theoretical setup is equivalent to Malus’ experimental setup in which both polarizers are placed on the same side of the light source (so the photons need to pass both polarizers in order to reach the target).

You can't just declare two setups "equivalent" when they clearly aren't, Bell's setup involved two measurements with polarizers made at a spacelike separation, not two successive measurements with polarizers on the same light beam. As I said there is no way in classical electromagnetism to reproduce the QM prediction of the cos^2 relationship for the correlations of these two spacelike-separated measurements, despite Malus' law, so it would simply be false to claim that a completely different setup with non spacelike-separated measurements was "equivalent" and therefore that the QM prediction could be "derived" from Malus' law.

 

[harrylin]

[..] Such critiques are soundly rejected because they end up modifying the Bell/EPR definitions beyond the point where they are meaningful.

As far as I know his critique has not been rejected but accepted*; and it appears to me that a refining of Bell's definitions as Nelson did after discussing it with Bell is very meaningful.

So basically, no one cares.

:uhh: Surely you mean that you don't care; for I do and so does Annalen der Physik!

[..] The point is that as you soften one element of Bell slightly, you open up opportunities/issues elsewhere. That may help us to better probe things. But it doesn't change Bell per se.

Indeed, that's the point!

*http://onlinelibrary.wiley.com/doi/10.1002/andp.200810345/abstract

 

[DrChinese]

As far as I know his critique has not been rejected but accepted...

If you think that is the definition of acceptance, then you are sadly mistaken. That alone counts for little, as I would expect you to know. I can cite any number of disproofs of Bell that have been published. I can also cite published disproofs of general relativity, evolution and the big bang.

Any way, start a thread if you want to discuss it rather than hijack another.

 

[JesseM]

As far as I know his critique has not been rejected but accepted*; and it appears to me that a refining of Bell's definitions as Nelson did after discussing it with Bell is very meaningful.

As I mentioned in post #123, Nelson acknowledged that his stochastic model can't reproduce the predictions of QM. http://www.mth.kcl.ac.uk/~streater/lostcauses.html#II which says:

I believe that Nelson's reason for giving the theory up was the difficulty in preventing action at a distance and the transmission of information faster than light. Doubts were expressed in the beautiful book, Quantum Fluctuations, by Edward Nelson, Princeton Series in Physics, 1985. Morato and Petroni surmise (page 5833) that it was the study of entangled states which turned Nelson against it.

Entangled states are the foundation of almost all versions of Bell inequality violations, so if stochastic mechanics can't reproduce QM predictions for entangled states it would seem to have questionable relevance to Bell's theorem.

Indeed, that's the point!

*http://onlinelibrary.wiley.com/doi/10.1002/andp.200810345/abstract

There's another paper here which responds to that one and claims to discount its conclusions:

http://onlinelibrary.wiley.com/doi/10.1002/andp.201010462/abstract
http://arxiv.org/abs/0910.4740

And then Schulz responds here:

http://arxiv.org/abs/0910.5660

 

[miosim]

You can't just declare two setups "equivalent" when they clearly aren't, Bell's setup involved two measurements with polarizers made at a spacelike separation, not two successive measurements with polarizers on the same light beam. As I said there is no way in classical electromagnetism to reproduce the QM prediction of the cos^2 relationship for the correlations of these two spacelike-separated measurements, despite Malus' law, so it would simply be false to claim that a completely different setup with non spacelike-separated measurements was "equivalent" and therefore that the QM prediction could be "derived" from Malus' law.

As I understand, QM predicts the same probability function for a pair of correlated photons to pass the corresponding polarizers in Bell/Aspect experiment as for a single photon to pass both polarizers in Malus’ experiment. The fact that the logic and math in both experiments correlate tells me that they describes the very similar physical phenomena.

I don't think "local realism" yields any specific function, I think the saw-like function is just meant to represent the closest you can come to the cos^2 function in local realism, as I explained in post #20.

I agree that different models of "local realism" may yield different specific functions. The critical part is that as long the particular function of "local realism" differs from the one predicted by QM, Bell’s inequity holds ground.

However, the supporters of Bell’s theorem are missing an elephant in the room because any model of "local realism" that yields a result that is different from QM cannot be in the “spirit of Einstein’s ideas” because he never questioned the correctness of QM, but its completeness and interpretation instead. Therefore Bell’s model of a "local realism" is a profound distortion of Einstein’s EPR argument

 

[JesseM]

As I understand, QM predicts the same probability function for a pair of correlated photons to pass the corresponding polarizers in Bell/Aspect experiment as for a single photon to pass both polarizers in Malus’ experiment. The fact that the logic and math in both experiments correlate tells me that they describes the very similar physical phenomena.

No, the "logic" is completely different in both experiments, even if the same equation is used. Again, Malus' law is derived from classical electromagnetism, but if you use the logic of classical electromagnetism to predict what will happen in a Bell type experiment where the two measurements are made at a spacelike separation, you can never reproduce the cos^2 relationship predicted by QM using the very different logic of a 2-particle wavefunction.

However, the supporters of Bell’s theorem are missing an elephant in the room because any model of "local realism" that yields a result that is different from QM cannot be in the “spirit of Einstein’s ideas” because he never questioned the correctness of QM, but its completeness and interpretation instead. Therefore Bell’s model of a "local realism" is a profound distortion of Einstein’s EPR argument

No, it isn't. You're missing the elephant in the room, which is that Einstein didn't know that it would be impossible for a local realistic theory to reproduce QM predictions, because Bell hadn't proved that while Einstein was alive. If you look at what Einstein was hoping for when he talked about a more complete explanation for QM, it seems he was thinking of a hidden variable theory based on exactly the same type of assumptions that physicists now call "local realism", the type of theory I was describing in 1) and 2) in [post=3245651]this post[/post]. I can give you quotes from Einstein's writings to support this, if you request.

 

[miosim]

...If you look at what Einstein was hoping for when he talked about a more complete explanation for QM, it seems he was thinking of a hidden variable theory based on exactly the same type of assumptions that physicists now call "local realism", the type of theory I was describing in 1) and 2) in [post=3245651]this post[/post]. I can give you quotes from Einstein's writings to support this, if you request.

Please provide quotes from Einstein's writings to support this.

 

[JesseM]

Please provide quotes from Einstein's writings to support this.

OK. In this post my comments will be in blue, quotes from Einstein and other authors in normal black text. Here are some quotes from a letter Einstein wrote to Schrödinger immediately after the EPR paper, saying that he thought the paper did not do such a good job explaining his point, and trying to clarify his own meaning with use of a helpful analogy. This is from pp. 167-168 of The Age of Entanglement by Louisa Gilder:

Einstein had not yet received Schrödinger's letter, when, on June 17, he wrote to him of Bohr's point of view: "I consider the renunciation of a spatio-temporal setting for real events to be idealistic, even spiritualistic. This epistemology-soaked orgy ought to burn itself out." He was not sure where Schrödinger stood in all of this: "No doubt, however, you smile at me and think that, after all, many a young whore turns into an old praying sister, and many a young revolutionary becomes an old reactionary."

The next day, Schrödinger's letter arrived, and Einstein thanked him for it, explaining that he had not written the paper himself and apologizing that it "did not come out as well as I had originally wanted; rather the essential thing was, so to speak, smothered by the formalism." For example, he explained, "I don't give a sausage" whether or not incompatible observables--Bohr's favorite subject--are involved.

It all came down to the relationship of Schrödinger's equation to reality. What is the connection between the mathematical description of events, and the events themselves? In what way does the Schrödinger wavefunction, ψ, reflect the actual state that a particle found itself in? Reality, or the particle's real situation, is represented in these discussions by the word state or the phrase state of affairs. The wavefunction, ψ, must represent this real state of affairs somehow. But it was hard to even articulate what was meant by such a connection to reality, or even what was meant by reality or state.

In his letter to Schrödinger, Einstein characteristically cut through this briar patch of linguistics with a parable. He wanted to illuminate the main point that had been obscured in the EPR paper. "In front of me stand two boxes, with lids that can be opened, and into which I can look when they are open. This looking is called 'making an observation.' In addition there is a ball, which can be found in one or the other of the two boxes where an observation is made. Now I describe a state of affairs as follows: The probability is one-half that the ball is in the first box." (This is all the Schrödinger equation will tell you.) "Is this a complete description?" asks Einstein, and then gives two different answers.

"NO: A complete description is: the ball is (or is not) in the first box...

"YES: Before I open the box the ball is not in one of the two boxes. Being in a definite box only comes about when I lift the covers...

"Naturally, the second 'spiritualist' or Schrödingerian interpretation is absurd," Einstein continued tactfully, "and the man on the street would only take the first, Bornian, interpretation seriously." Born might not have recognized his interpretation, which Einstein seemed to be using in this description only as far as he wanted to, but presumably Bohr would have recognized himself, even without being named: "But the Talmudic philosopher whistles at 'Reality' as at a bugaboo of naïveté, and declares that the two conceptions differ only in their mode of expression...

"One cannot get at the Talmudist if one does not make use of a supplementary principle: the separation principle," Einstein explains. "The contents of the second box are independent of what happens to the first. If one holds fast to the separation principle, only the Born description is possible, but not it is incomplete."

So I think it's fairly clear that Einstein is saying that if you have a scenario like this:

--Experimenters are performing a certain type of measurement on two objects (boxes or particles) and we find that they are guaranteed to get perfectly correlated results with probability 1 (like the guarantee that if one experimenter opens his box and gets the result "saw a ball", that must mean that when the other experimenter opened her box she got the result "didn't see a ball)

Then if we believe in the "separation principle" saying that any properties of one object immediately before measurement are independent of what happens to the other object, we must conclude that before measurement both objects had properties which predetermined the results they'd give, with the predetermined results being perfectly correlated (in terms of boxes, this just means that before either was opened there was already a definite truth that one had a ball inside and the other didn't, and the property of having a ball inside predetermines the measurement result "saw a ball" while the property of not having a ball inside predetermines the measurement result "didn't see a ball"). So the separation principle and the perfectly correlated results together imply there are local properties associated with each object before measurement, properties that predetermine their responses to being measured. And if the wavefunction does not specify these properties, then either the wavefunction is giving an incomplete description of the full physical state of each object, or the separation principle is false. But it's clear from the above that Einstein was on the side of the separation principle being true and the completeness of the wavefunction being false, he calls it "absurd" to advocate an interpretation where there is no definite truth about what's in each box until they're opened, and mocks this interpretation as being the argument of a "Talmudic philosopher".

Arthur Fine also talks about this letter in his book The Shaky Game: Einstein Realism and the Quantum Theory, and after describing Einstein's two-box scenario, goes on to say on pp. 36-37:

Einstein continues in this letter to give a technical reformulation of the EPR argument. It is a little confusing because it introduces a further refinement of the idea of completeness (this time in terms of state functions correlated to real states of affairs). But I think there is enough material contained, as it were, in Einstein's boxes to give at least one formulation of some of the essentials of EPR that were obscured by Podolsky's exposition.

Consider the system of two particles correlated via the conservation law for total linear momentum. Separation is the claim that whether a physical property holds for one of the particles does not depend on measurements (or other interactions) made on the other particle when the pair is widely separated in space. Completeness is the claim that if a certain physical property in fact holds for one particle at a given time, then the state function for the combined system at that time should yield probability one for finding that the property does hold (i.e., the subsystem consisting of the particle should have a state function which is an eigenstate for the property in question).

One can now copy Einstein's box argument as follows. Suppose the two particles (A and B) are far apart and I measure, say, particle A for linear momentum (in a certain direction). Using the conservation law I can infer the linear momentum of particle B from the result of this measurement on A. Thus after the A measurement, the B particle has a certain linear momentum. By separation, this real property of B must have held already at the time when I began my measurement on A (or just before, in the case of instantaneous measurement). For otherwise I would have created the momentum at B by measuring A, in violation of separation. But at the initial moment of the A measurement, the state of the composite system does not yield probability one for finding any momentum value for B, for that state is a nontrivial superposition of products of "momentum eigenstates" for the A and B subsystems. Hence the description provided by the state function given by quantum theory is incomplete. Here, as in the illustration, the argument establishes the incompatibility of separation and completeness.

It is this incompatibility that I take to be the central conclusion, which got obscured in EPR. Many years later, in Schilpp (1949, p. 682) Einstein put it succinctly in these words:

the paradox forces us to relinquish one of the following two assertions:
(1) the description by means of the ψ-function is complete
(2) the real states of spatially separated objects are independent of each other.

It is important to notice that the conclusion Einstein draws from EPR is not a categorical claim for the incompleteness of quantum theory. It is rather that the theory poses a dilemma between completeness and separation; both cannot be true. It is also important to notice that the argument I have drawn from Einstein's illustration does not depend in any way on simultaneous measurements or even attributions of position and momentum. The argument depends on the satisfaction of a single conservation law and the inferences drawn from that concerning the measurement of a single variable. This feature of the situation, I believe, is completely buried in the original paper and, because of that, Einstein's ideas concerning completeness and separation have become needlessly entangled with discussions of the uncertainty formulas and hidden variables. In his letter to Schrödinger of June 19, 1935, Einstein says that if the argument he gives applies to pairs of incompatible observables "ist mir wurst," which I would translate loosely as "I couldn't care less." The argument nowhere depends on that, nor do the basic ideas.

Although Fine says that the basic argument was just to show the incompatibility of completeness and separation, as I noted above Einstein clearly favored keeping separation and throwing out the idea that the wavefunction provides a complete description (i.e. there must be other properties not specified by the wavefunction)...on p. 38 Fine also writes:

Einstein wanted to use the dilemma posed by EPR to show that if we maintain the ideas of action-by-contact embodied in the separation principle, then we must view quantum theory as providing no more than a statistical account of the realm of objects whose properties outstrip the descriptive apparatus of the theory. As we have seen, he felt that the concepts needed to describe these properties adequately would be other than the dynamical concepts of classical physics. Thus, although Einstein took the incompleteness to be a sign that something better was required, he never showed any interest in the hidden variables program for filling out the theory from within.

I think the point being made here is that although he thought that the wavefunction description was incomplete so some form of extra variables (whether "hidden" or potentially measurable by some technique not dreamed of by quantum physicists) would be needed in a more complete description, probably he didn't think this was likely to just involve assigning values to the conventional quantum variables like position and momentum in cases where the wavefunction doesn't specify their values, he was hoping the variables would be of some new type.

In terms of the box analogy, one might imagine that instead of one box containing a ball before being opened, they both contain computers connected to holographic projectors, and the computers can sense when the lid is being opened and depending on their programming they will either respond by projecting an image of a ball, or projecting the image of an empty box. In this case the local variables associated with each box would not consist of "ball" or "no ball", but rather would be a detailed specification of the programming of each computer. But it would still be true based on the separation principle and the perfect correlation between results that if one was programmed to project a ball when the box was opened, that must mean the other was programmed to project an empty box, so the local variables (the program of each computer) would still predetermine the fact that one would give the measurement result "saw a ball" and the other would give the result "didn't see a ball".

Note that this sort of thing is quite possible in my assumptions 1) and 2) (which as I said I think are just a restatement of Bell's assumptions), since 1) says nothing specific about what the "local facts" actually are. In the example of measuring the momentum of two entangled particles, all that's necessary for a perfect correlation is that whatever the local facts are that cause a measurement of one particle to reveal a momentum p, the local facts associated with the other particle must also such that if a momentum measurement is made on it, it will yield result -p.

The idea that Einstein didn't want the "extra" (possibly hidden) variables to just be specification of the values of unmeasured quantum-mechanical properties is also suggested by this quote from p. 57, which is discussing Einstein's idea that the wavefunction just stands for a statistical ensemble of possible complete descriptions of the state:

This suggestion, that his remarks about ensembles constitute a kind of hidden variables theory, was actually put to Einstein in a letter from Aron Kupperman (November 10, 1954). In his reply Einstein does not deny the connection but rather downplays its significance by writing as follows, "I think it is not possible to get rid of the statistical character of the present quantum theory by merely adding something to the latter, without changing the fundamental concepts about the whole structure" (letter of November 14, 1954; from the English draft).

And on p. 58 Fine quotes Einstein's "Autobiographical Notes":

It is my opinion that the contemporary quantum theory by means of certain definitely laid down basic concepts, which on the whole have been taken over from classical mechanics, constitutes an optimal formulation of the connections. I believe, however, that this theory offers no useful point of departure for future developments. (Schilpp 1949, p. 87)

Finally on pp. 60-61 Fine describes what he understands as Einstein's idea of locality:

Einstein's several reworking of the EPR situation certainly involve a locality principle. It is this:

Einstein-locality. The real, physical state of one system is not immediately influenced by the kinds of measurements directly made on the second system, which is sufficiently spatially separated from the first.

I think my citations in the paper establish that this formulation is Einstein's. It differs from Bell's just over what it is that is not supposed to be influenced at a distance. For Bell it is the outcomes of the measurements of certain quantum observables (like spin). For Einstein it is the "real, physical states." In his various writings Einstein says even less about the nature of these postulated real states than the says about his ensemble interpretation, and for good reason. He was urging others, and struggling himself, to build a new theory that would "discover these states, i.e. invent them. Whatever these states are, they would indeed (in Einstein's conception, at least) determine the real physical variables and, most likely, the outcomes of measurement of these. But Einstein is very clear that, in his opinion, the quantum mechanical variables (the "observables") are the wrong ones. They are not the real physical variables, and that is why it is hopeless to try to complete quantum theory from within.

I agree with Fine about the idea that the real physical states need not involve conventional QM observables like momentum (again think of my analogy in which the real state is the programming of a computer which can either project an image of a ball or an empty box when the box is opened), but I disagree that Bell's formulation was any different, see my comments in the second-to-last paragraph of [post=3264303]post #142[/post] explaining why I think that my notion of a theory involving an unspecified collection of "local facts" is equivalent to Bell's talk of "local beables".

I should also note that Fine thinks there is some possibility of getting around Bell's theorem by use of a "prism model" in which some particles are intrinsically "defective" for certain types of measurements, so if we try to measure a given property (like spin in a particular direction) some fraction of the particles just won't show up in our measurements and thus won't be included in our dataset, which means the choice of what to measure can no longer be considered independent of the properties that the particle had immediately before measurement in our dataset (if this is unclear, billschnieder explained this type of model in terms of my own lotto card analogy in posts [post=2767632]113[/post] and [post=2767828]115[/post] on an older thread). Bell does assume in most of his proofs that there is no correlation between particle properties before measurement and the choice of detector setting, but it seems to me that these prism models would be themselves contradict the predictions of QM, so they aren't really relevant to a theoretical proof showing that local realism is incompatible with QM. But in terms of the possibility that something like this could be true experimentally, I think this loophole is just one version of what's called the"detection efficency loophole", and there are modified versions of Bell inequalities which take into account that not all particle pairs are successfully measured, see here. There have been Bell tests with ions that managed to close the detector efficiency loophole, see [post=2851208]this post[/post], although they didn't simultaneously close the locality loophole (though experiments with photons have closed that one, none have yet closed both simultaneously. It seems pretty unlikely that we could have a non-contrived-looking local realist theory where both types of loopholes were being exploited at once, though.)

 

[harrylin]

[..] There's another paper here which responds to that one and claims to discount its conclusions:
http://onlinelibrary.wiley.com/doi/10.1002/andp.201010462/abstract
http://arxiv.org/abs/0910.4740

And then Schulz responds here:
http://arxiv.org/abs/0910.5660

Thanks Jesse for trying; however it's besides the point. Schultz, Schmelzer and the reviewers accept Nelson's critique/precision concerning "passive locality". Regretfully I still don't understand what it means. As nobody here could answer that question I now started a dedicated thread on it.
https://www.physicsforums.com/showthread.php?t=494057
Please don't further comment on my question in this thread.

Regards,
Harald

 

[JesseM]

"One cannot get at the Talmudist if one does not make use of a supplementary principle: the separation principle," Einstein explains. "The contents of the second box are independent of what happens to the first. If one holds fast to the separation principle, only the Born description is possible, but not it is incomplete."

Little typo here which makes the last part of Einstein's quote confusing, it should read "but now it is incomplete".

 

[miosim]

JesseM,

Sorry for the late response.
I don’t see how the references you presented demonstrate that Einstein rejected the mathematical formalism of QM as incorrect. Only in this case Bell could justify that his “local realism” matches with Einstein views.
From http://en.wikipedia.org/wiki/EPR_paradox
“…Einstein struggled to the end of his life for a theory that could better comply with causality, protesting against the view that there exists no objective physical reality other than that which is revealed through measurement interpreted in terms of quantum mechanical formalism…”
Regarding Bell’s theorem, the only thing I don’t understand is how his theory was accepted by the scientific community. His inability to offer a reasonable model of “local realism” that would match Einstein’s views, his jumping to a conclusion about the non-existence of the realistic model that would match with QM formalism, and the end jumping to a conclusion about the “influence over distance” that at the same time contradicts with the widely accepted theory of relativity – all this seemed childish to me.
I am done with Bell’s theorem. You may not believe this but I didn’t understand it when I started this thread, so I wasn’t faking in my introductory post asking for help.

Thanks,
Mark

P.S.
I hope to return in a month or so to discuss new interpretation of quantum mechanics including my interpretation of Bell’s experiment.

 

[JesseM]

JesseM,

Sorry for the late response.
I don’t see how the references you presented demonstrate that Einstein rejected the mathematical formalism of QM as incorrect. Only in this case Bell could justify that his “local realism” matches with Einstein views.

Sigh. Why would Einstein have needed to think "the mathematical formalism of QM is incorrect" even if he had the same notion of local realism as Bell? Bell hadn't yet proved that there needed to be any inconsistency between Einstein's version of local realism--identical to my 1) and 2), and identical to Bell's "local causality--and "the mathematical formalism of QM". I already explained this concept to you, read it again a few times until it sinks in:

No, it isn't. You're missing the elephant in the room, which is that Einstein didn't know that it would be impossible for a local realistic theory to reproduce QM predictions, because Bell hadn't proved that while Einstein was alive. If you look at what Einstein was hoping for when he talked about a more complete explanation for QM, it seems he was thinking of a hidden variable theory based on exactly the same type of assumptions that physicists now call "local realism", the type of theory I was describing in 1) and 2) in [post=3245651]this post[/post]. I can give you quotes from Einstein's writings to support this, if you request.

Then after I wrote that last sentence there, you took me up on the offer to actually post some quotes, but now in your most recent post I see you've completely dropped the subject of whether Einstein's assumptions were the same as 1) and 2) (the specific claim I was offering to provide evidence for when I said "I can give you quotes from Einstein's writing to support this"), and instead decided to just mindlessly repeat the same confused arguments you made before. Guess I shouldn't have wasted my time, should have known better than to confuse you with a person who is actually interested in thoughtful discussion of the issues.

Regarding Bell’s theorem, the only thing I don’t understand is how his theory was accepted by the scientific community. His inability to offer a reasonable model of “local realism” that would match Einstein’s views

So you aren't even going to tell me if you think Einstein's conception is any different from my 1) and 2), or whether you think Bell's conception is different from my 1) and 2)? It's easy to stick with the same preconceptions you had from the start if you refuse to actually answer detailed questions or think about specifics, and just stick to vague sweeping statements and pompous claims about it being "childish".

I am done with Bell’s theorem. You may not believe this but I didn’t understand it when I started this thread

I believe you still don't understand it, as evidenced by the fact that you thought my 1) and 2) were not equivalent to it, and the fact that you were continually making false statements like that it assumes a "classical deterministic corpuscular model of the photons" (it doesn't).

 

[billschnieder]

2. The local facts about any given point P in spacetime are only causally influenced by facts about points in the past light cone of P, meaning if you already know the complete information about all points in some spacelike cross-section of the past light cone, additional knowledge about points at a spacelike separation from P cannot alter your prediction about what happens at P itself (your prediction may be a probabilistic one if the laws of physics are non-deterministic).

It is a logical contradiction to say you will still make a probabilistic prediction even if you already have complete information about the event. Unless by probabilistic you mean a probability of 0 or 1, which is infact not a 'probability' but a 'certainty'. Assigning a probability to an event implies there is a degree of uncertainty involved which means there is missing information. You can therefore not claim to know everything (ie have complete information) about the event at the same time! Determinism has nothing to do with this, as incomplete information about deterministic laws will give you probabilistic results.

The words "complete" as used by EPR in the phrase "complete theory" and as used in the phrase "complete information" above have the same meaning. As concerns what the EPR claims about the meaning of reality, the following statement is quite clear:

Whatever the meaning assigned to the term complete, the following requirement for a complete theory seems to be a necessary one: every element of physical reality must have a counterpart in the physical theory.
...
If, without in any way disturbing a system, we can predict with certainty (ie with probability equal to unity) the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity.

So clearly, any definition of "element of physical reality" which is "probabilistic" is foreign to the EPR one.

As concerns locality, it has been shown that Bell's inequality can be satisfied by a system in which non-local information transfer is imposed, contrary to popular belief, and calling into question claims that Bell's inequality somehow faithfully represent the EPR requirement for locality.

Bell's inequality violation due to misidentification of spatially non-stationary random processes
Louis Sica. Journal of Modern Optics, 1362-3044, Volume 50, Issue 15, 2003, Pages 2465 – 2474
----

The connection between Bell's inequalities based on probabilities and those based on correlations
Author: Louis Sicaa

Abstract
Violation of Bell inequalities is widely regarded as a definitive test for non-locality. However, Bell correlational inequalities must always be satisfied by all jointly present, cross-correlated data. The correlations of variable pairs obtained in repeated runs are not cross-correlated in this way and are not required to satisfy the Bell inequality. In addition, by using information regarded as non-local, proper joint correlations may be computed among counterfactual and measured variables. These correlations satisfy the Bell inequality, but are spatially non-stationary in angle. By using a simple symmetry condition, such considerations may be extended to inequalities in probabilities. The latter may be derived directly from correlational inequalities developed by Clauser, Horne, Shimony and Holt (CHSH). Violation of either correlational or probabilistic Bell inequalities then implies that the Bell correlation cannot be accounted for by a stochastic process that is spatially stationary in angle coordinates. However, other processes may still be allowed.

An additional point to be made about point (2) above is the fact that is conflates or does not clearly distinguish between single events and multiple events. QM does not and can not make predictions about single individual events. It only makes predictions about the results obtained when many different events have been accumulated.

It has been shown by Barut almost 10 years ago, that carefully distinguishing between individual events and ensembles of events is sufficient to debunk the "no-hidden variable theorems".

A. O. Barut Foundations of Physics, Vol. 22, No. 1, 1992 "How to Avoid "Quantum Paradoxes"

Conclusion:
We have seen that all major "no-hidden variable theorems" involve two or more spins, and make use of the tacit assumption (not even stated that it is an assumption) that each individual spin component has dichotomic +/- 1/2 value for every single event. We believe that this assumption, which is correct for repeated events, i.e., for polarized beams, is not correct for single events. Modifying it, we not only obtain correct EPR-spin correlations, but also avoid the so-called quantum paradoxes, without changing the results of standard quantum theory which only applies to repeated events.

 

[DrChinese]

... As concerns locality, it has been shown that Bell's inequality can be satisfied by a system in which non-local information transfer is imposed, contrary to popular belief.

It has been shown by Barut almost 10 years ago, that carefully distinguishing between individual events and ensembles of events is sufficient to debunk the "no-hidden variable theorems".

A. O. Barut Foundations of Physics, Vol. 22, No. 1, 1992 "How to Avoid "Quantum Paradoxes"

Your references are grossly inadequate and go against generally accepted science. I notice that you are again hijacking a thread to make arguments against Bell, when the purpose here was to understand Bell.

Please stick to forum guidelines and take this to Independent Research. Or write a paper and get it published.

 

[JesseM]

2. The local facts about any given point P in spacetime are only causally influenced by facts about points in the past light cone of P, meaning if you already know the complete information about all points in some spacelike cross-section of the past light cone, additional knowledge about points at a spacelike separation from P cannot alter your prediction about what happens at P itself (your prediction may be a probabilistic one if the laws of physics are non-deterministic).

It is a logical contradiction to say you will still make a probabilistic prediction even if you already have complete information about the event.

Try reading more carefully, I didn't say anything about "complete information about the event", I said "if you already know the complete information about all points in some spacelike cross-section of the past light cone, additional knowledge about points at a spacelike separation from P cannot alter your prediction about what happens at P itself".

Bell also defined local causality in terms of complete cross-sections of the past light cone of events, see my summary of his "La nouvelle cuisine" paper in [post=3248153]this post[/post] which includes links to the majority of the text of the paper on google books. In particular, look at the diagram Bell includes at the top of this page, where either boundary of region 3 of the diagram represents the type of "spacelike cross-section of the past light cone" I was referring to, and Bell defines local causality to mean that if you know the complete set of information about all local facts in region 3 (he calls them "local beables"), then further information about region 2 will not alter your predictions about what happens in region 1. He formalizes this idea on this later page, where the combination of c and λ represent all local beables in region 3, "a" represents some detector setting in region 1 while "A" represents some measurement outcome in region 1, similarly "b" is a detector setting in region 2 while "B" is a measurement outcome in region 2...then local causality can be expressed as the condition that P(A|B,a,b,c,λ)=P(A|a,c,λ).

The words "complete" as used by EPR in the phrase "complete theory" and as used in the phrase "complete information" above have the same meaning. As concerns what the EPR claims about the meaning of reality, the following statement is quite clear:

If, without in any way disturbing a system, we can predict with certainty (ie with probability equal to unity) the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity.

So clearly, any definition of "element of physical reality" which is "probabilistic" is foreign to the EPR one.

Nonsense, they only say that if you can predict with probability 1 what a measurement will yield (as is true if you measure one member of an entangled pair and are making a prediction about the other member), then "there exists an element of physical reality corresponding to this physical quantity". This does not imply the converse, that if there is an element of physical reality corresponding to what you are going to measure, it must automatically be possible to predict with probability 1 what the result will be at some time prior to the measurement. The EPR statement is true under my assumptions 1) and 2) about "local realism" which you are responding to (for reference they are detailed in [post=3231977]this post[/post]), the converse statement is not true under my assumptions, if you know of any statement in the EPR paper suggesting they would disagree please point it out.

As concerns locality, it has been shown that Bell's inequality can be satisfied by a system in which non-local information transfer is imposed, contrary to popular belief

Again you seem confused about some principles of logical reasoning, saying "X implies Y" does not automatically mean "Y implies X" or equivalently "Y cannot be true if ~X" (here Y=Bell inequalities satisfied, X=local realism, and ~X=failure of local realism...in your earlier misconceived argument, Y=an element of physical reality corresponding to some quantity, and ~X=impossible to predict value of that quantity in advance)

An additional point to be made about point (2) above is the fact that is conflates or does not clearly distinguish between single events and multiple events.

I defined "local facts" to mean facts about a single point in spacetime, but I added the following clarification to show we could still talk about facts involving an extended region:

Keep in mind that 1) doesn't forbid you from talking about "facts" that involve an extended region of spacetime, it just says that these facts must be possible to deduce as a function of all the local facts in that region. For example, in classical electromagnetism we can talk about the magnetic flux through an extended 2D surface of arbitrary size, this is not itself a local quantity, but the total flux is simply a function of all the local magnetic vectors at each point on the surface, that's the sort of thing I meant when I said in 1) that all physical facts "can be broken down into a set of local facts". Similarly in certain Bell inequalities one considers the expectation values for the product of the two results (each one represented as either +1 or -1), obviously this product is not itself a local fact, but it's a trivial function of the two local facts about the result each experimenter got.

 

[billschnieder]

Your references are grossly inadequate and go against generally accepted science. I notice that you are again hijacking a thread to make arguments against Bell, when the purpose here was to understand Bell.

Please stick to forum guidelines and take this to Independent Research. Or write a paper and get it published.

Everything mentioned above is material published in peer-reviewed journals and I have provided the citations to back them up. There is nothing independent in that. Perhaps you could point to what criteria you use for "adequacy" of references which hopefully is more than the fact that you do not like them.

There were claims made in this thread about what EPR meant by local realism, and what Bell meant by Local realism and how equivalent the two are. My response simply highlighted and emphasized aspects of the EPR position (in their own words) which I believe were being overlooked, with additional references backing up my points.

I understand that you do not like what I wrote. Which is not equivalent to violating forum guidelines.

It was stated that according to EPR you can know complete information and still your prediction may be a probabilistic one if the laws of physics are non-deterministic. I simply quoted the words from the original EPR paper to show that this statement is false and at best contrary to published EPR position. Do you have anything to say about this? Or you would rather I shut up let false statements like these stand.

 

[billschnieder]

Whatever the meaning assigned to the term complete, the following requirement for a complete theory seems to be a necessary one: every element of physical reality must have a counterpart in the physical theory.
...
If, without in any way disturbing a system, we can predict with certainty (ie with probability equal to unity) the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity.

Nonsense, they only say that if you can predict with probability 1 what a measurement will yield (as is true if you measure one member of an entangled pair and are making a prediction about the other member), then "there exists an element of physical reality corresponding to this physical quantity". This does not imply the converse, that if there is an element of physical reality corresponding to what you are going to measure, it must automatically be possible to predict with probability 1 what the result will be at some time prior to the measurement.

After adding back the full quote, including the first part which you conveniently left out, it is clear from the quoted EPR statements above that there is no place for "probabilistic" predictions in a complete theory, if you have complete information.

If every element of physical reality is present in the theory and you can predict every one of them with certainty, then you have complete information. Obviously according to the second part of the quote, you will not call it an element of physical reality if you can not predict it with certainty. Where then will your "probabilistic" prediction come from?

Any thing else is at odds with the EPR position, that's all I'm saying.

 

[JesseM]

After adding back the full quote, including the first part which you conveniently left out, it is clear from the quoted EPR statements above that there is no place for "probabilistic" predictions in a complete theory, if you have complete information.

You're still misunderstanding, if you know all the elements of reality in a given region of spacetime then you know the results of all measurements in that region with probability 1, but that doesn't imply if you know all the elements of reality in the past of that region (like "region 3" in the past of "region 1" in Bell's diagram), the results of measurements in the region must always be "determined" with probability 1. The idea of the EPR paper is that if you know with probability 1 what result you will get before you actually make the measurement, then there must already be elements of reality which determine that measurement result. This could still be true in a theory which contained some stochastic elements, just look at Einstein's example of the ball that's placed in one of two boxes, he's saying that since opening one box allows you to predict with probability 1 the result of opening the other, that means that even before you open the other box there are "elements of reality" inside that box which predetermine what you'll see--in this example, these would be assumed to just be the presence or absence of a ball inside the closed box. But that doesn't imply every aspect of the inside of the box is deterministic, for example the ball might be vibrating slightly and the vibrations could contain a genuinely random element. If there was no way to predict with probability 1 how it would vibrate at a time before we actually measured the vibrations, then prior to the time of measurement there need not have been any element of physical reality that predetermined what measurement result we would later get.

 

[edguy99]

...You can't just declare two setups "equivalent" when they clearly aren't, Bell's setup involved two measurements with polarizers made at a spacelike separation, not two successive measurements with polarizers on the same light beam. As I said there is no way in classical electromagnetism to reproduce the QM prediction of the cos^2 relationship for the correlations of these two spacelike-separated measurements, despite Malus' law, so it would simply be false to claim that a completely different setup with non spacelike-separated measurements was "equivalent" and therefore that the QM prediction could be "derived" from Malus' law.

I think I may have lost myself in this discussion, would you mind explaining or posting a link for the type of setup you have in mind?

 

[DrChinese]

I think I may have lost myself in this discussion, would you mind explaining or posting a link for the type of setup you have in mind?

JesseM is correctly pointing out that Malus' cos^2 and the QM prediction of cos^2 - are the same only by "coincidence" (there is a relationship but it is not straightforward to obtain). An LR model can - in fact must - deliver other results. The devil is in the details. If you have an LR model, it is on you to demonstrate it is local realistic as no one will believe you. Well, billschnieder might.

 

[DrChinese]

I think I may have lost myself in this discussion, would you mind explaining or posting a link for the type of setup you have in mind?

http://arxiv.org/abs/quant-ph/0205171

"We use polarization-entangled photon pairs to demonstrate quantum nonlocality in an experiment suitable for advanced undergraduates. The photons are produced by spontaneous parametric downconversion using a violet diode laser and two nonlinear crystals. The polarization state of the photons is tunable. Using an entangled state analogous to that described in the Einstein-Podolsky-Rosen ``paradox,'' we demonstrate strong polarization correlations of the entangled photons. Bell's idea of a hidden variable theory is presented by way of an example and compared to the quantum prediction. A test of the Clauser, Horne, Shimony and Holt version of the Bell inequality finds $S = 2.307 , in clear contradiction of hidden variable theories. The experiments described can be performed in an afternoon. "

 

[billschnieder]

You're still misunderstanding,

No you are.

if you know all the elements of reality in a given region of spacetime then you know the results of all measurements in that region with probability 1, but that doesn't imply if you know all the elements of reality in the past of that region (like "region 3" in the past of "region 1" in Bell's diagram), the results of measurements in the region must always be "determined" with probability 1.

The idea of the EPR paper is that if you know with probability 1 what result you will get before you actually make the measurement, then there must already be elements of reality which determine that measurement result.

What you are misunderstanding is the fact that the idea of hidden variables/elements of reality is tightly coupled with determinism and completeness. In a deterministic theory, if any two histories (or models) in the theory have identical state variables at time t=t0, then they have identical state variables at all times. (see Determinism and Probability in Physics, Peter Clark and Jeremy Butterfield, Proceedings of the Aristotelian Society, Supplementary Volumes, Vol. 61, (1987), pp. 185-243 )

In such a theory, if you know the complete state of the system at a given point, it will be possible in principle to predict with certainty the state at any future point. Probabilities or uncertainties only arise in such a theory, if you do not have complete information.

This could still be true in a theory which contained some stochastic elements

This is not true. To say that the theory is stochastic and at the same time say that you can predict with certainty is a contradiction. On the one hand you are saying you have complete information, and on the other hand you are saying you do not.

just look at Einstein's example of the ball that's placed in one of two boxes, he's saying that since opening one box allows you to predict with probability 1 the result of opening the other, that means that even before you open the other box there are "elements of reality" inside that box which predetermine what you'll see --in this example, these would be assumed to just be the presence or absence of a ball inside the closed box. But that doesn't imply every aspect of the inside of the box is deterministic, for example the ball might be vibrating slightly and the vibrations could contain a genuinely random element. If there was no way to predict with probability 1 how it would vibrate at a time before we actually measured the vibrations, then prior to the time of measurement there need not have been any element of physical reality that predetermined what measurement result we would later get.

But this is misleading because the "theory" in this example is simply presence or absence of the ball, and has nothing to do with vibrations of the ball in the Box. Even so, complete information about the the ball in the box will then have to include more state variables specifying it's vibration, in which case you will still not obtain "probabilistic" results. If you mean that you can have complete information about presence of the ball and yet not have complete information about the vibrations of the ball, then you are effectively using a different theory for presence and a different one for vibrations. And since the presence or absence in a box have nothing to do with vibrations, additional information about the vibrations will not alter your prediction about presence or absence of the ball in the box. Therefore, it still doesn't make sense why you will give this example to back up your claim that your prediction can be probabilistic even with complete information.

You can not escape from the fact that "complete information/certainty" and "uncertainty/probability" are incompatible concepts. Unless you are referring to complete information about one thing, and uncertainty about an entirely different thing.

The main point remains therefore that according to EPR there is no place for "probabilistic" predictions in a complete theory, if you have complete information.

 

[JesseM]

What you are misunderstanding is the fact that the idea of hidden variables/elements of reality is tightly coupled with determinism and completeness. In a deterministic theory, if any two histories (or models) in the theory have identical state variables at time t=t0, then they have identical state variables at all times. (see Determinism and Probability in Physics, Peter Clark and Jeremy Butterfield, Proceedings of the Aristotelian Society, Supplementary Volumes, Vol. 61, (1987), pp. 185-243 )

Yes, I know what "determinism" means, it's pointless to provide an academic citation for this since we are not disagreeing on the basic definition of determinism.

This is not true. To say that the theory is stochastic and at the same time say that you can predict with certainty is a contradiction.

I didn't make the over-broad claim you accuse me of, you seem to be implying a false dichotomy between the possibilities "everything is stochastic, nothing can be predicted with certainty" and "everything is deterministic, everything can be predicted with certainty given sufficient knowledge of past conditions". What I was actually arguing was that you could have a theory where there are some stochastic elements but in certain situations it may still be possible to predict the outcome of a measurement with complete certainty. And I was also trying to make my definition of local realism as broad as possible, so it could be used to derive inequalities that would apply even in a situation where you don't see perfect correlations between separated measurements, for more on this point see below.

But this is misleading because the "theory" in this example is simply presence or absence of the ball, and has nothing to do with vibrations of the ball in the Box.

I didn't say the two were related! Similarly in the case of a stochastic local realistic theory that attempts to explain perfect correlations between measurements of some property like momentum, the stochastic element of the theory would have nothing to do with the momentum of these particles, which must be predetermined prior to measurement. Did you think I was saying otherwise? If so you misread me, I didn't suggest any stochastic element in the value of a specific quantity that was being found to have a perfect correlation (but that's if such a perfectly correlated quantity is assumed at all, which is something we may not want to assume if we are being as general as possible--again, see below).

Even so, complete information about the the ball in the box will then have to include more state variables specifying it's vibration, in which case you will still not obtain "probabilistic" results. If you mean that you can have complete information about presence of the ball and yet not have complete information about the vibrations of the ball, then you are effectively using a different theory for presence and a different one for vibrations.

No, it needn't involve multiple theories. You could have a single theory describing the motion of the molecules that make up the ball, which both allows their paths to have a degree of randomness but also forbids them from "tunneling" through a potential barrier like the walls of the box.

Therefore, it still doesn't make sense why you will give this example to back up your claim that your prediction can be probabilistic even with complete information.

Prediction of what can be probabilistic? If there is a perfect correlation between two measurements of some property like momentum, then any local realist theory which attempts to explain this must say that before they were measured, the local variables associated with each particle already completely predetermined what their momentum would be if measured, there is no "probabilistic" element there. But there may be other elements that are probabilistic, and likewise it may not be true in the first place that such a perfect correlation exists. But I think maybe now I see the source of the confusion between us (and I accept some of the blame for it), you were referring to this statement of mine:

2. The local facts about any given point P in spacetime are only causally influenced by facts about points in the past light cone of P, meaning if you already know the complete information about all points in some spacelike cross-section of the past light cone, additional knowledge about points at a spacelike separation from P cannot alter your prediction about what happens at P itself (your prediction may be a probabilistic one if the laws of physics are non-deterministic).

In this statement, I was attempting to be as general as Bell in my definition of local realism--some of the inequalities he derived did not depend on the assumption of a perfect correlation between separated measurements, and thus in some of his papers he defined "local causality" in as broad a way as possible so that knowledge of past conditions would not predetermine the measurement results with perfect certainty. I agree, as would Bell, that if you are looking at one of the inequalities that does assume a perfect correlation between measurements with the same detector setting, in that case it must be true that the measurement outcome was predetermined prior to measurements, that there is no probabilistic element at all. This conclusion can in fact be derived from the more general assumptions about local realism, which is why it doesn't need to be a starting assumption if you want to make your proof as general as possible.

In the "La nouvelle cuisine" paper I referred you to earlier (again see [post=3248153]this post[/post]), Bell was in fact deriving an inequality that doesn't assume perfect correlations, see here:

http://www.scholarpedia.org/article...Bell.27s_theorem_without_perfect_correlations (this article notes that the CHSH inequality is identical to the one Bell derived on p. 7 of this paper, equation 16, and you can see that's the same as the inequality 6.10.4 on this page of the "La nouvelle cuisine" paper)

Of course QM does predict perfect correlations in some situations, so if you're only interested in the theoretical question of whether QM is compatible with local realism, you're free to assume that such correlations exist just as EPR did (and as Bell did in some earlier papers) in that case we must say that complete knowledge of a cross-section of the past light cone of one measurement after the two light cones no longer overlap (like region 3 in Bell's diagram here) must indeed predetermine the outcome of any measurement, I agree that there can be no probabilistic element in the specific case of variables that are perfectly correlated this way. But if you want to come up with an inequality that you intend to test experimentally, it may be more useful to use one that does not assume "perfect" correlations since realistically you may not to be able to verify that this is true experimentally.

Related to this, I recently came across this paper which seems to have a very careful and precise discussion of Bell's assumptions in the "La nouvelle cuisine" paper, and on p. 11 the author notes:

There is, in particular, a tendency for a relatively superficial focus on the relatively formal aspects of Bell’s arguments, to lead commentators astray. For example, how many commentators have too-quickly breezed through the prosaic first section of Bell’s 1964 paper (p. 14-21) – where his reliance on the EPR argument “from locality to deterministic hidden variables” is made clear – and simply jumped ahead to section 2’s Equation 1 (p. 15), hence erroneously inferring (and subsequently reporting to other physicists and ultimately teaching to students) that the derivation “begins with deterministic hidden variables”? (1981, p. 157)

I agree with the author that in both Bell's first paper and in the EPR paper, the idea that the values of measured properties are predetermined is not a starting assumption, but rather something that is concluded if you have perfect correlations between separated measurements and if we assume the underlying theory involves only local causality (i.e. assuming a theory that respects conditions 1 and 2 from my [post=3231977]earlier post[/post], which as I [post=3270631]argued before[/post] are ones that I think Einstein would have accepted based on his comments).

edit: I see Bell also discusses his own and Einstein's opinion on determinism not being assumed at the outset on pp. 7-8 of the Bertlmann's socks paper (starting with the paragraph on p. 7 that begins, "It is important to note that to the limited degree that determinism plays a role in the EPR argument, it is not assumed but inferred.")

 

[miosim]

JesseM,

I can’t answer your lengthy comments, because I have a narrow bandwidth of a time and abilities. Therefore I can handle only one task at a time, but and I am not sure to which of your comments I should respond first.

While reading your exchange with billschnieder I am wondering if the mathematics and the formalized logic are adequate tools to prove or disprove a reality. I think that a common language could handle this task much better. For me a reality is the stuff that happens regarding can we observe it or not and this, as I understand, is the position of Einstein about physical reality.

For Bohr and Heisenberg there is no physical reality if we can’t observe or measure it.
According to Bohr "…There is no quantum world. There is only an abstract quantum mechanical description. It is wrong to think that the task of physics is to find out how Nature is”
And for Heisenberg “… the atoms or the elementary particles are not ... real they form a world of potentialities or possibilities rather than one of things or facts”.

For those who faithfully follow Bohr and Heisenberg philosophy, they contradict to them self by trying to describe their non-real universe in term of real processes like influence over distance. They don’t have to do this because their task isn’t about explaining what happens inside this “unreal block box”, because allegedly nothing happens there and therefore their QM is complete.

Fort those who follow the Einstein’s philosophy the QM aren’t complete until they explain what actually happens inside this “real QM black box”. For these scientists there is plenty of work to do.

 

[JesseM]

I can’t answer your lengthy comments, because I have a narrow bandwidth of a time and abilities. Therefore I can handle only one task at a time, but and I am not sure to which of your comments I should respond first.

My comments to you in [post=3273668]post 156[/post] were not particularly lengthy. Anyway, you could start by addressing whether you see any reason to think Einstein's assumptions (which I quoted in [post=3270631]this post[/post], hopefully you had time to at least read it) differed from my 1) and 2), and if so where exactly.

For me a reality is the stuff that happens regarding can we observe it or not and this, as I understand, is the position of Einstein about physical reality.

Yes, and that's what the "local facts" in my 1) and 2) are supposed to represent, as well as Bell's "local beables". They needn't be anything directly observable, they are the real local facts about each local point in spacetime. They represent things like whether a sealed box has a ball inside it or not before we look in it, to use Einstein's example.

For those who faithfully follow Bohr and Heisenberg philosophy, they contradict to them self by trying to describe their non-real universe in term of real processes like influence over distance. They don’t have to do this because their task isn’t about explaining what happens inside this “unreal block box”, because allegedly nothing happens there and therefore their QM is complete.

You are totally confused if you think Bell was following Bohr, his intent was the opposite, to examine the features a theory would need if it purported to tell us what was really going on with quantum particles when they're not being measured.

Fort those who follow the Einstein’s philosophy the QM aren’t complete until they explain what actually happens inside this “real QM black box”. For these scientists there is plenty of work to do.

Yes, and this was Bell's philosophy as well, but thanks to him we know that anyone who wants a theory of what's really going on must accept that it cannot be a local theory (unless it violates some other of Bell's assumptions, like allowing the experimenter to split into multiple parallel versions, or allowing backwards-in-time causal influences).

 

[JDoolin]

I have trouble with the very basics of what is supposedly being measured. I gather that you're basically measuring polarizations, but I'm not sure it makes sense.

The choice the observer has is to set up an apparatus. And apparently he can set up this apparatus in three different ways. One to detect an up or down, one to detect a left or right, and one to detect a forward and backward.

But as far as I can tell the diagrams don't explain physically what they are setting up...just in the abstract--that there are three different variables that can be measured.

But I never see an actual photograph of the physical set-up of the laboratories where they are doing these measurments. I never hear a description of the physical materials that are being used. For instance, is there a you-tube video where you can actually watch people with actual equipment (not just a cartoon, or animations) performing this experiment?

 

[mayflow]

Einstein said that you don't truly understand something unless you can explain it to your Grandma. I think that this should apply also to a grandpa.
I am a grandpa who is struggling to understand the Bell's Theorem. I read a number of popular books and articles, tryed Wikipedia, followed discussions on this forum, and even tried to read the original Bells’ paper, but I still cannot grasp the logic and the experimental proof of this theorem. The popular explanation of the experiment in terms of red and blue balls may be a good illustration but still doesn’t make sense to me as an explanation.
Of cause my inability to understand math is a biggest problem, but the controversial concepts of quantum mechanics don’t give me such a problem regardless that they are also based on math.
In spite of my shallow background in math (say high school level) I believe that this shouldn’t prohibit me to understand the physical concept assosiated with this theorem.
Actually, I view math as a formalized logic and logic works only within well defined area of knowledge. Therefore I am careful with the logical and mathematical deductions applied to subatomic events that are obviously not fully understood yet.
So I am asking for a help in understanding the Bell's theorem and its experimental proof in terms of physical concepts (of cause if we truly understand them). For the start I have a specific questions: How come the formalism of quantum theory leads to the Sine correlation while EPR formalism leads to Linear correlation (see Fig.below)?

Bell simply states that a photon or whatever once it is entangled
with another, supersedes time and space and can instantaneously interreact, no matter the supposed time or space distances, as if time and space do not factually exist, because they most likely don't.

 

[miosim]

My comments to you in post 156 were not particularly lengthy. Anyway, you could start by addressing whether you see any reason to think Einstein's assumptions (which I quoted in this post, hopefully you had time to at least read it) differed from my 1) and 2), and if so where exactly…

1. The complete set of physical facts about any region of spacetime can be broken down into a set of local facts about the value of variables at each point in that regions (like the value of the electric and magnetic field vectors at each point in classical electromagnetism)

2. The local facts about any given point P in spacetime are only causally influenced by facts about points in the past light cone of P, meaning if you already know the complete information about all points in some spacelike cross-section of the past light cone, additional knowledge about points at a spacelike separation from P cannot alter your prediction about what happens at P itself (your prediction may be a probabilistic one if the laws of physics are non-deterministic).

Sorry but I cannot answer this question because 1) and 2) are two “technical” for me and the comments of Arthur Fine are too gossip-like for me to trust him. When I asked you to provide quotes from Einstein's I expect a direct Einstein’s writing and not an interpretation.

As I understand, the main goal of Einstein is to return a reality to physics by providing a meaning interpretation to QM formalism. EPR paper, was just one rhetorical argument (and may be not the best one) in favor of this view.
By the way, I don’t believe that a knowledge about the characteristic (spin, polarization, etc.) of one particle yields the complement characteristic of the the correlated particle (but for different reason than imposed by Copenhagen Interpretation) and I think that Einstein may accept this if this non-deterministic behavior will be explained within the framework of physical reality.

They needn't be anything directly observable, they are the real local facts about each local point in spacetime. They represent things like whether a sealed box has a ball inside it or not before we look in it, to use Einstein's example.

“Sealed box” and other illustrative examples like Alice, Bob etc. are adding one more layer of interpretation and misinterpretation and in my opinion their use may cause more problems than help.

You are totally confused if you think Bell was following Bohr, his intent was the opposite, to examine the features a theory would need if it purported to tell us what was really going on with quantum particles when they're not being measured. ).

Indeed it seems that Bell was sympathetic to Einstein ideas. However the passion with which Bell proclaimed impossibility of local realism and existence on non-locality (as inevitable) tell me that his conclusion was predetermined by strong influence of Copenhagen Interpretation.

Yes, and this was Bell's philosophy as well, but thanks to him we know that anyone who wants a theory of what's really going on must accept that it cannot be a local theory (unless it violates some other of Bell's assumptions, like allowing the experimenter to split into multiple parallel versions, or allowing backwards-in-time causal influences).

Amen

 

[Philip000]

One problem highlighted by Bell is the paradoxical use of language by theorists
Most seem to use observation and measurement as interchangeable terms when they are not, and for me, it is the non understanding of terms of agreement that causes confusion.

Observations can be said to be commonsense, in as much as each of us, or even a mechanical device, can sense something in some way, and measurement can be said to be a comparison of the observations made.

If I am point A then point B is removed from me, and I can invent a device or tool of measurement to establish the distance of removal.
The same is true of every other measurement, and point A can exist beyond me and others by general agreement with them, and a distance measurement such as one yard between A and B can be established as a tool of imperial measurement.
However, the measurement is not superior to the observation, and in fact the observation is always part of any measurement just as commonsense is.

Tools of measurement, are imagined, invented, replicated, mechanised, atomized, devised and compromised, but the basic facts of point A and B still exist, no matter how many other points are included into one measurement and no matter how many tools of measurement are added together to form a new measurement.
Movement is a commonsense observation, even as speed of movement, and it becomes a complex measurement that uses measurements of time and distance to establish its veracity. Every complex measurement relies on other measurements and all of them rely on the observation of points A and B and the agreements that established the tools of measurement.

Bell’s theorem initially relies on two observations, the observable results of a series reading taken at point A and the observable results at point B. They are different, and the only tool of measurement used to define what exists between them is the % of difference that the reading of B is from A. The same is true in reverse and whatever the % difference that B is from A would be the same that A is from B.

Commonsense says that if these observations and a measurement of the difference between A and B observations in a reversed, handed world were taken, then if what was measured was the same in the non reversed world, the results would be identical.
This is the meat of the EPR experiment, and it allows an observer in the non reversed world to predict what a result will be in a handed and reversed world.

Predictability is an essential part of calculation, 2 + 2 always = 4 and calculating differences is the same as calculating that an addition of two numerically based measurements will always be the same.

In the EPR experiment, all factors in the reversed and non reversed worlds are shown to be identical, therefore the results of the same measurement taken in each world are predictable from the other world.

This predictability is inbuilt into measurements because the tool or device of measurement ensures it.
A yard may fluctuate in the material world due to a changing environment, but the yard of measurement never fluctuates and it never changes because it has been established, by agreement, as the difference between point A and point B in the abstract world of like minded people.
Distance exists as an observation, agreement verifies the distance as a measurement and this like minded agreement gives science an inflexible tool of abstract measurement, but its use still relies on the commonsense observations of A and B.

In the EPR experiment, the difference between A and B is established as a fact in the handed reversed and non reversed worlds, and the problem that Bell comes up with is one of calculations based on these facts, not that the facts exist.
Calculations are predictions, and Bell tries to say that an addition of 2 + 2 as measurements taken in the reversed and non reversed worlds does not = 4.

He does this by first making an assumption, that 2 + 2 = 4, then by saying that this is not proven by experiment, and that an inequality exists which shows that 2 + 2 = (6).
This (6) is said to be proven to exist by an experiment, in which another measurement has been taken between the worlds, and yet all that has happened is that point A of one of the original observations has been moved to a new point C, to give an unrelated result and the measurement has actually been taken between (B reversed which is now C in the non reversed world) and B (non reversed.).
In effect his theory is a slight of hand conjuring trick, a bit like a pea under a nutshell being shifted without anyone noticing it has changed position

What moves faster than light is predictability, the ability to calculate the result of a measurement, even light years away, in a matter of seconds, or even instantly if the calculation has already been made, by the use of inflexibly established, like minded measurement and calculation tools.
This is what the EPR experiment was about, and what it intended to show was that the method of calculating what happens in the quantum world, by using probability, is inadequate to describe the quantum world’s observable and measureable reality.

The quantum world is observable, it’s observations can be measured as points A and B, but the measurements cannot be calculated as a fixed abstract prediction because the tools used to predict its events rely on probability calculations, and not on fixed, established likeminded facts.
Einstein said the quantum world is predictable, Bohr said it is not, and Bell came up with an illusion of his own device to add confusion to their disagreement..

In making calculations today, it seems to be quite easy to ignore points A and B, as Bell’s theory of a non commonsense inequality demonstrates, but without the common sense of observation and the points it establishes, measurement and calculation get lost in the machinations of invented and seemingly established theoretical misunderstandings.

 

[miosim]

Bell simply states that a photon or whatever once it is entangled
with another, supersedes time and space and can instantaneously interreact, no matter the supposed time or space distances, as if time and space do not factually exist, because they most likely don't.

And this way Bell's theorem violates the well accepted theory of relativity and in the same time introduces the mysterious “action on distance” phenomena. Therefore one who introduces (or supports) such “theory” should have a good explanation of this contradiction. Until then it should be treaded as antiscientific or at least as a highly speculative hypothesis only.

However I can’t blame Bell and other with such uncritical acceptance of the “action on distance” concept, because of another famous historical precedent. I mean the “wave function” collapse (the “action on distance” is routed in) that demonstrates that the physical phenomena that define a common sense a logic could be replaced with a ”scientifically sound label” pretending that science accomplished its role in explaining nature.

My main point in this post is that the “action on distance” is just an extreme case of the “wave function collapse” and therefore acceptance or rejection of the Bell’s theorem may depend on our acceptance or rejection of the “wave function collapse.”

 

[Jonathan Scott]

And this way Bell's theorem violates the well accepted theory of relativity and in the same time introduces the mysterious “action on distance” phenomena. Therefore one who introduces (or supports) such “theory” should have a good explanation of this contradiction. Until then it should be treaded as antiscientific or at least as a highly speculative hypothesis only.

You do persist in missing the point, don't you?

Bell's theorem itself is very simple and very robust. It proves that either QM is wrong or the assumption of local realism (which is normally taken as part of Special Relativity) is wrong. It basically boils down to the fact that the differences between sets A and C cannot exceed the sum of the differences between sets A and B and between sets B and C, regardless of the physical models which gave rise to these results.

As the relevant parts of QM are very strongly supported by experiment, this means that it is almost certainly the assumption of local realism which is wrong. This is obviously very disturbing and unexpected, and it does indeed conflict with the principle of relativity. Scientists are therefore interested in trying to understand exactly how QM violates local realism, and whether there might be some underlying inner mechanism that would help to explain how it works.