FrediFizzx wrote:So here you have it folks. There can be no further doubt that QM is in fact local for the EPR-Bohm scenario!
Using eigenvalues, Jay's manifestly local measurement functions are essentially equivalent to the following upon implementing the polarizer functions.
where is the hidden variable. This is more of the beginning of "The New Quantum Mechanics".
.
FrediFizzx wrote:Did you read Jay's new paper?
.
gill1109 wrote:FrediFizzx wrote:Did you read Jay's new paper?
.
Not yet in detail.
He can also answer my questions, if you can't. And I will read the paper, soon...
I don't see the formulas you quote in the paper.
FrediFizzx wrote:gill1109 wrote:FrediFizzx wrote:Did you read Jay's new paper?
.
Not yet in detail.
He can also answer my questions, if you can't. And I will read the paper, soon...
I don't see the formulas you quote in the paper.
Eqs. (16) and (17). The answers to your questions are really obvious. You basically answered them yourself.
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gill1109 wrote:FrediFizzx wrote:So here you have it folks. There can be no further doubt that QM is in fact local for the EPR-Bohm scenario!
Using eigenvalues, Jay's manifestly local measurement functions are essentially equivalent to the following upon implementing the polarizer functions.
where is the hidden variable. This is more of the beginning of "The New Quantum Mechanics".
.
Can you confirm my reading of this, that sequence of equalities here allows us to deduce
rather similar to formulas which I saw before in the writings of J.S. Bell?
gill1109 wrote:Is it true that the right-hand sides do not depend on the hidden variable ,. . .
gill1109 wrote:. . . but do depend on another (hidden?) variable ?
gill1109 wrote:And that ?
Yablon wrote:gill1109 wrote:Can you confirm my reading of this, that sequence of equalities here allows us to deduce
rather similar to formulas which I saw before in the writings of J.S. Bell?
Yes.
[...]
Jay
Heinera wrote:Yablon wrote:gill1109 wrote:Can you confirm my reading of this, that sequence of equalities here allows us to deduce
rather similar to formulas which I saw before in the writings of J.S. Bell?
Yes.
[...]
Jay
But this is just Bell's example (9) in his original paper. And we know that this does not reproduce the quantum correlations; in fact the correlation in this case can be shown to be , where is the angle between the detector settings.
FrediFizzx wrote:Well, if you do the product calculation, A*B, you have (+/-1)(+/-1) = (+/-1).
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Heinera wrote:FrediFizzx wrote:Well, if you do the product calculation, A*B, you have (+/-1)(+/-1) = (+/-1).
.
Well, that was an extremely rudimentary calculation. It is of course possible to do much better than that, by evaluating the integral
.
gill1109 wrote:. . . I had already seen (16) and (17). But these equations don't make any sense. A term which clearly depends on a, s and h is stated to be equal to a term which only depends on a and h. These equations must be wrong. Or only true in special circumstances.
And a limit in which "s" occurs as a dummy variable is supposed to be equal to an expression in which "s" is still present. This is just gobbeldly-gook. Jay has got to get back to the drawing board.
[No disrepect intended! Just my opinion. it's forty-five years since I did calculus 101]
Yablon wrote:gill1109 wrote:. . . I had already seen (16) and (17). But these equations don't make any sense. A term which clearly depends on a, s and h is stated to be equal to a term which only depends on a and h. These equations must be wrong. Or only true in special circumstances.
And a limit in which "s" occurs as a dummy variable is supposed to be equal to an expression in which "s" is still present. This is just gobbeldly-gook. Jay has got to get back to the drawing board.
[No disrepect intended! Just my opinion. it's forty-five years since I did calculus 101]
Hi Richard,
I do not believe I have to go back to the drawing board. But, I will agree that there is a lot to be discussed, and the questions you raised are fair questions.
So, let's take this all a step at a time. Below I have reproduced my equation (1) and a like-equation (1) for b. These are the Pauli identities.
Q1: Do you agree that these are correct equations when the vectors a and s are in the same Hilbert space for (1), and when s and b are in the same Hilbert space for (1) for b?
Next, I have written (16) and (17) to only show the part before the right arrow, and to show that (16) is a function of a, s and h, and that (17) is a function of s, b and h.
Q2: Do you agree that these contain correct calculations of the eigenvalues for the two equations (1), and that in general they are properly written down, including that h=+1 and h=-1 represent the two possible eigenvalues based on the Pauli matrices being 2x2 operators?
Q3: Though I did not show the calculation because it is a standard calculation, do you have any reason to disbelieve, when the two related eigenstates are normalized to sum to 1, and using the probabilistic interpretations customarily applied to 2x2 operators in quantum mechanics, that there is a 50% probability for h=+1 and 50% for h=-1?
Let me also ask on more thing:
Q4: Expressions such as sgn (a dot s) = +/-1 appear regularly in the EPRB literature. When you see such an expression, what does it mean to you, physically?
Let's go from there.
Jay
FrediFizzx wrote:Heinera wrote:FrediFizzx wrote:Well, if you do the product calculation, A*B, you have (+/-1)(+/-1) = (+/-1).
.
Well, that was an extremely rudimentary calculation. It is of course possible to do much better than that, by evaluating the integral
.
Well, I don't think you are doing something right because I get,
.
Heinera wrote:FrediFizzx wrote:Heinera wrote:FrediFizzx wrote:Well, if you do the product calculation, A*B, you have (+/-1)(+/-1) = (+/-1).
.
Well, that was an extremely rudimentary calculation. It is of course possible to do much better than that, by evaluating the integral
.
Well, I don't think you are doing something right because I get,
.
This makes absolutely no sense. There is not much point in discussing Bell's theorem if you don't understand integrals. For a correct evaluation of the integral, see Peres eqn. (6.21) on page 161.
Heinera wrote:FrediFizzx wrote:Well, if you do the product calculation, A*B, you have (+/-1)(+/-1) = (+/-1).
.
Well, that was an extremely rudimentary calculation. It is of course possible to do much better than that, by evaluating the integral
.
gill1109 wrote:Heinera wrote:FrediFizzx wrote:Well, if you do the product calculation, A*B, you have (+/-1)(+/-1) = (+/-1).
.
Well, that was an extremely rudimentary calculation. It is of course possible to do much better than that, by evaluating the integral
.
Your notation is not very good. If it were true, I would write something like
where is the uniform Haar measure on the sphere .
gill1109 wrote:One certainly does have to worry about the sign. The devil is in the details. One also has to worry about Mathematica's precise rules for evaluating mathematical expressions, and how Mathematica interprets multiple occurrences of +/- and -/+
gill1109 wrote:Dear Jay, dear friends
I respond to the matters of notation.
Note that Jay’s bold a, b and s are vectors in R^3. They are not operators on the same Hilbert space.
His bold sigma is a vector of three 2x2 matrices
His “Id” is the 2x2 identity matrix
All his 2x2 matrices can be thought of as operators on the same complex Hilbert space of dimension 2
There is (up to isomorphism) only one 2-dimensional Hilbert space and we may represent it with C^2
I have no problems with his equation (1)
There is a bold a in the middle expression of its unnumbered friend which can’t be right. But the outside equality (first expression equals third) is just rewriting (1) with roles of some vectors replaced and multiplying throughout by minus one.
Equations (1) and its friend (corrected) are therefore just two times the same familiar identity, just changing names of things in a consistent way on left and right hand sides; please fix the middle expression of the second identity
Equations (16) and (17) are, I take it, definitions. The notation is obscure. Why does lambda have two subscripts *and* three arguments? If on the right hand sides one merges h with s, one could take (16) as definition of something which has just two arguments, or just two subscripts (but not both) (depending on which notation one prefers). (17) is superfluous since it is just a different way to say the same thing, similar to Jay’s rewriting of (1) as its companion unnumbered equation.
One could also define something which has which has just three arguments, or just three subscripts (but not both).
Jay’s paper, his notation!
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