FrediFizzx wrote:I think the thing Jay is working on at RW actually proves the bound on Bell-CHSH is |0|. Notice how Heine, Parrott, etc. were trying to get Jay to change it so that the averages would be something other than 0 for each of the four expectation terms.
In my humble opinion, the next step that needs to be taken based on my earlier datasets is to postulate “local realism.” Specifically, we postulate that all of the 4 values A, A’, B, B’ for any given slip in the “slip dataset” *actually do exist in reality*
minkwe wrote:Jay Yablon wrote:In my humble opinion, the next step that needs to be taken based on my earlier datasets is to postulate “local realism.” Specifically, we postulate that all of the 4 values A, A’, B, B’ for any given slip in the “slip dataset” *actually do exist in reality*
Somebody should tell Jay that he is wasting his time, unmeasured values do not exist in reality. They are imaginary.
viewtopic.php?f=21&t=34
EDIT:
I see that Joy already thoroughly explained it in his last post
Joy Christian wrote:
I have had some time to reflect on Jay’s latest installment and now I know what is wrong with it. The definition of realism he has implicitly used — which is essentially the one assumed by the followers of Bell — is unjustifiably more restrictive than the one envisaged by Einstein.
Let me try to bring out what is wrong with it as transparently as I can. To this end, let me write the CHSH string of expectation values in the following form:
Int_K A B rho(k) dk + Int_K A B’ rho(k) dk + Int_K A’ B rho(k) dk – Int_K A’ B’ rho(k) dk . … (1)
This expression is both mathematically and physically equivalent to the expression
Int_K { A( B + B’ ) + A'( B – B’ ) } rho(k) dk , …………………. (2)
where Int_K stands for an integration over the space K of the hidden variables k.
Since the above two integral expressions are identical to each other, there is no loss of generality if we use the second expression to bring out the unjustified assumption in Jay’s definition of realism (which, as I have stressed, is essentially that of the followers of Bell).
To begin with, the second expression, equation (2), involves an integration over fictitious quantities like A( B + B’ ) and A'( B – B’ ). These quantities are not parts of the space of all possible measurement outcomes A, A’, B, B’, etc., because that space is not closed under addition. This is analogous to the fact that the set D = {1, 2, 3, 4, 5, 6} of all possible outcomes of a die throw is not closed under addition. 3+6, for example, is not a part of D.
But there is also a much more serious physical problem with the definition of realism assumed by Jay. As I have stressed before, the quantity A( B + B’ ) does not represent any meaningful element of any possible physical world, classical or quantum. This is because B and B’ can coexist with A only counterfactually. If B coexists with A, then B’ cannot coexist with A, and vice versa. But in his analysis Jay implicitly assumes that B and B’ can both coexist with A simultaneously. This would be analogous to my being in New York and Miami at exactly the same time. But no reasonable definition of realism can justify such an unphysical demand. The notion of realism envisaged by Einstein most certainly does not demand any such thing.
Finally, note that Jay does not have to actually use expression (2) in his analysis for it to be wrong. He can restrict his analysis to expression (1) only and it would still be wrong, because, as noted, (1) and (2) are both mathematically and physically identical.
Dirkman wrote:The topic on retractionwatch seems to have almost 500 comments, I wonder if it is the most discussed topic ever on retractionwatch.
Joy Christian wrote:Dirkman wrote:The topic on retractionwatch seems to have almost 500 comments, I wonder if it is the most discussed topic ever on retractionwatch.
I bet it is!
***
minkwe wrote:Joy Christian wrote:Dirkman wrote:The topic on retractionwatch seems to have almost 500 comments, I wonder if it is the most discussed topic ever on retractionwatch.
I bet it is!
***
Hopefully, after your excellent explanation, it is becoming obvious to a few of the participants that there is a difference between doing mathematics, and doing physics. They think because they can measure <AB>, <AB'>, <A'B> and <A'B'> independently in physically meaningfully ways, they assume it is okay to add them up and ascribe any kind of physical meaning to the sum.
50+ years lost because of such trivial errors.
Consider now the proof of von Neumann that dispersion free states, and so hidden variables, are impossible. His essential assumption is: Any real linear combination of any two Hermitian operators represents an observable, and the same linear combination of expectation values is the expectation value of the combination. This is true for quantum mechanical states; it is required by von Neumann of the hypothetical dispersion free states also. In the two-dimensional example of Sec. 11, the expectation value must then be a linear function of α and β. But for a dispersion free state (which has no statistical character) the expectation value of an observable must equal one of its eigenvalues. The eigenvalues (2) are certainly not linear in β. Therefore, dispersion free states are impossible. If the state space has more dimensions, we can always consider a two-dimensional subspace; therefore, the demonstration is quite general.
The essential assumption can be criticized as follows. At first sight the required additivity of expectation values seems very reasonable, and it is rather the nonadditivity of allowed values (eigenvalues) which requires explanation. Of course the explanation is well known: A measurement of a sum of noncommuting observables cannot be made by combining trivially the results of separate observations on the two terms -- it requires a quite distinct experiment. For example the measurement of σx, for a magnetic particle might be made with a suitably oriented Stern Gerlach magnet. The measurement of σy, would require a different orientation, and of (σx+σy) a third and different orientation. But this explanation of the nonadditivity of allowed values also establishes the nontriviality of the additivity of expectation values. The latter is a quite peculiar property of quantum mechanical states, not to be expected a priori. There is no reason to demand it individually of the hypothetical dispersion free states, whose function it is to reproduce the measurable peculiarities of quantum mechanics when averaged over. Thus the formal proof of von Neumann does not justify his informal conclusion: "...". It was not the objective measurable predictions of quantum mechanics which ruled out hidden variables. It was the arbitrary assumption of a particular (and impossible) relation between the results of incompatible measurements either of which might be made on a given occasion but only one of which can in fact be made. ... The danger in fact was not in the explicit but in the implicit assumptions. It was tacitly assumed that measurement of an observable must yield the same value independently of what other measurements may be made simultaneously. Thus as well as P(ϕ3) say, one might measure either P(ϕ2) or P(ψ2), where and ϕ2 and ψ2 are orthogonal to ϕ3 but not to one another. These different possibilities require different experimental arrangements; there is no a priori reason to believe that the results for P(ϕ3) should be the same. The result of an observation may reasonably depend not only on the state of the system (including hidden variables) but also on the complete disposition of the apparatus;
Bell interview in Omni magazine wrote:Bell:Then in 1932 [mathematician] John von Neumann gave a “rigorous” mathematical proof stating that you couldn’t find a nonstatistical theory that would give the same predictions as quantum
mechanics. That von Neumann proof in itself is one that must someday be the subject of a Ph.D. thesis for a history student. Its reception was quite remarkable. The literature is full of respectable
references to “the brilliant proof of von Neumann;” but I do not believe it could have been read at that time by more than two or three people.
Omni: Why is that?
Bell: The physicists didn’t want to be bothered with the idea that maybe quantum theory is only provisional. A horn of plenty had been spilled before them, and every physicist could find something to apply quantum mechanics to. They were pleased to think that this great mathematician had shown it was so. Yet the Von Neumann proof, if you actually come to grips with it, falls apart in your hands! There is nothing to it. It’s not just flawed, it’s silly. If you look at the assumptions it made, it does not hold up for a moment. It’s the work of a mathematician, and he makes assumptions that have a mathematical symmetry to them. When you translate them into terms of physical disposition, they’re nonsense. You may quote me on that: the proof of von Neumann is not merely false but foolish.
minkwe wrote:Bell: The physicists didn’t want to be bothered with the idea that maybe quantum theory is only provisional. A horn of plenty had been spilled before them, and every physicist could find something to apply quantum mechanics to. They were pleased to think that this great mathematician had shown it was so. Yet the von Neumann proof, if you actually come to grips with it, falls apart in your hands! There is nothing to it. It’s not just flawed, it’s silly. If you look at the assumptions it made, it does not hold up for a moment. It’s the work of a mathematician, and he makes assumptions that have a mathematical symmetry to them. When you translate them into terms of physical disposition, they’re nonsense. You may quote me on that: the proof of von Neumann is not merely false but foolish.
Bell dug a grave for von Neumann, then turned around and buried himself in it, and you have a long line of sheeple lining up to join him in the grave. (Note the distinction Bell makes between mathematical and physical arguments).
Richard Gill wrote:
Einstein’s local realism demands that A(a), A(a’), B(b) and B(b’) simultaneously exist as elements of reality. Hence A(a)*{ B(b) + B(b’ ) } + A(a’ )*{ B(b) – B(b’ ) } exists.
Joy Christian wrote:We are in a far worse situation than in the case of von Neumann's theorem. Let alone mathematicians, in the case of Bell's theorem physicists have allowed themselves to be misguided by an aggressive and persistent statistician who is willing to stoop to any level of academic thuggery to maintain his fanatic beliefs in the "theorem.":Richard Gill wrote:
Einstein’s local realism demands that A(a), A(a’), B(b) and B(b’) simultaneously exist as elements of reality. Hence A(a)*{ B(b) + B(b’ ) } + A(a’ )*{ B(b) – B(b’ ) } exists.
But by no means, as Bell would say. A(a)*{ B(b) + B(b’ ) } + A(a’ )*{ B(b) – B(b’ ) } simply does not exist even if A(a), A(a’), B(b) and B(b’) exist as elements of reality.
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FrediFizzx wrote:I can imagine there will be a flurry of objections to what Jay has posted on RW tomorrow. Time to shift gears... get them to try to prove that Jay's eq. (6) could be true. LOL!
FrediFizzx wrote:I can imagine there will be a flurry of objections to what Jay has posted on RW tomorrow. Time to shift gears... get them to try to prove that Jay's eq. (6) could be true. LOL!
ajw wrote:The CSHS derivation might be wrong (I am not arguing that) but there are many simulations that tried to beat the 2 limit, and only succeeded when leaving a part of the data out of the result set. How does this relate to this discussion, am I missing something?
ajw wrote:They do try to get the negative cos, but then they often give the CSHS as a measure of their success. Like in Adenier https://arxiv.org/pdf/quant-ph/0306045v6.pdf or De Raedt http://rugth30.phys.rug.nl/pdf/COMPHY3339.pdf. My original reference simulation was based on the latter.
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