As concerns Graft's paper, where the heck did equations (1) and (2) come from. They couldn't possibly be from Jaynes' or Bell's papers. He should fix the blatant error in equations (1) and (2). See Jayne's equation (12) and (13) in the article cited by Jaynes.
Secondly, it's quite astonishing how Jaynes' elegant argument has been misrepresented by the likes of Gill (who is quoted in the above article). Jaynes argument has 4 main points:
1. Bell says "It would be very remarkable if
b proved to be a causal factor for A, or
a for B; i.e., if P(A|aλ) depended on b or P(B|bλ) depended on a. But
according to quantum mechanics, such a dilemma can happen. Moreover, this peculiar long-range influence in question seems to go faster than light"
2. But Jaynes argues, according to QM, P(B|ab) = P(B|b) = 1/2 for all a,b. Therefore, Bell is dead wrong that according to QM P(B|bλ) can depend on a.
That is, QM is not consistent with remote parameter dependence.3. Jaynes also argues that according to QM P(B|Aab) = (1-cos θ)/2. Therefore in trying to complete QM with hidden variables, Bell introduced the schism with QM by assuming that P(B|Aab) = P(B|ab) = P(B|b). Therefore, according to Jaynes, there are many easier and more cogent tests that could be performed to test this experimentally.
Jaynes wrote:Equation (14) is, therefore, the point where Bell introduces a conflict with QM. Recognizing this, it is evident that one could produce any number of experimental tests where the predictions of QM conflict with various predictions of (14). The particular set of inequalities given by Bell is only one example of this, and not even the most cogent one. We shall leave it as an exercise for the reader to show that, at this point, application of Bayesian principles would have yielded a
significance test for (14) that is more powerful than the Bell inequalities
4. Outcome dependence such as the case in QM P(B|Aab) =/= P(B|ab), cannot in general be interpreted as physical causation (see Bernouli's urn example in Jaynes paper).
Many of the discussions in Graft's paper would have benefited from a fuller understanding of Jaynes, than the caricature being spread around by Gill.
As concerns Graft's paper, where the heck did equations (1) and (2) come from. They couldn't possibly be from Jaynes' or Bell's papers. He should fix the blatant error in equations (1) and (2). See Jayne's equation (12) and (13) in the article cited by Jaynes.
Secondly, it's quite astonishing how Jaynes' elegant argument has been misrepresented by the likes of Gill (who is quoted in the above article). Jaynes argument has 4 main points:
1. Bell says "It would be very remarkable if [i]b[/i] proved to be a causal factor for A, or [i]a[/i] for B; i.e., if P(A|aλ) depended on b or P(B|bλ) depended on a. But
according to quantum mechanics, such a dilemma can happen. Moreover, this peculiar long-range influence in question seems to go faster than light"
2. But Jaynes argues, according to QM, P(B|ab) = P(B|b) = 1/2 for all a,b. Therefore, Bell is dead wrong that according to QM P(B|bλ) can depend on a. [u]That is, QM is not consistent with remote parameter dependence.[/u]
3. Jaynes also argues that according to QM P(B|Aab) = (1-cos θ)/2. Therefore in trying to complete QM with hidden variables, Bell introduced the schism with QM by assuming that P(B|Aab) = P(B|ab) = P(B|b). Therefore, according to Jaynes, there are many easier and more cogent tests that could be performed to test this experimentally.
[quote="Jaynes"]Equation (14) is, therefore, the point where Bell introduces a conflict with QM. Recognizing this, it is evident that one could produce any number of experimental tests where the predictions of QM conflict with various predictions of (14). The particular set of inequalities given by Bell is only one example of this, and not even the most cogent one. We shall leave it as an exercise for the reader to show that, at this point, application of Bayesian principles would have yielded a
significance test for (14) that is more powerful than the Bell inequalities[/quote]
4. Outcome dependence such as the case in QM P(B|Aab) =/= P(B|ab), cannot in general be interpreted as physical causation (see Bernouli's urn example in Jaynes paper).
Many of the discussions in Graft's paper would have benefited from a fuller understanding of Jaynes, than the caricature being spread around by Gill.
