Richard,
Apologies for this delayed reply. Among other things, I've been trying to make sense of your math, etc. Including the Boole-based work that you repeat (the post above) after I refuted it (3 posts above).
gill1109 wrote:Gordon, you are still completely blind to the main point. Bell’s elementary probability follows from [?? GW emphasis] some elementary but controversial physical assumptions (nowadays called local realism).
Let's identify this as "
Richard Gill's main point". And let's recall that I have already [3 posts above], refuted "Gill's better-way" of probabilistically deriving the Bell and CHSH-Bell inequalities.
As for Bell: I say that "elementary probability" begins best with expectations: the averages that we learn about in primary school.
And surely that's where QM excels and Bell begins: see Bell 1964:(2)! And surely you've seen that that's where I continue when refuting your "better-way"?
Thus, in short: "
Richard Gill's main point" is back-to-front and quite silly. For, rather than
following from some elementary but controversial physical assumptions (nowadays called local realism), Bell’s "elementary probability"
begins correctly ––– via (2) and (14a) –– with two valid expectations: AND ––– independent of any physical assumptions ––– continues
erroneously to invoke a third expectation in the next line, (14b).
So, with Bell's first error being his move from (14a) to (14b): please explain the "controversial physical assumptions" that Bell uses. It's not enough to say "local realism" without you define each term. Further, if you say that Bell uses "naive realism" — how is it that Bell and Bellians are still on the horns of a dilemma 25 years later? (See endnote below.) Kids have normally rejected "naive realism" by the age of 10.
gill1109 wrote:You (like Bohr) disagree with those physics assumptions.
I've said before: I disagree with Bohr on some related issues. So please specify the Bohrian assumption that you think I agree with.
gill1109 wrote:Nature violates the inequalities, hence Bell’s (correct, elementary) math and logic proves that the physics assumptions of local realism are indeed, as you say, naïeve.
When you define Bell's version of "local realism" we might agree on Bell's naivety. BUT I show that "Bell’s (correct, elementary) math and logic" is FALSE, independent of any theorising.
gill1109 wrote: Not just naïeve: they must be wrong. You, me, and Bell agree on this.
They are, indeed, wrong. So let's get it clear about Bell's naivety; see above. For, as I see it: I disagree with you [your "better-way" is false] and I disagree with Bell [his MATH is false; his 1990 dilemma rather silly (see below)].
gill1109 wrote:Bell is not silly. But lots of people are too silly to follow his argument.
Maybe.
In Bell's words,
25 years after the publication of his theorem, with my emphasis:
p.5: ‘I cannot say that action at a distance (AAD is required in physics. But I can say that you cannot get way with no AAD. You cannot separate off what happens in one place and what happens in another. Somehow they have to be described and explained jointly.’ p.6: ‘The Einstein program fails, that’s too bad for Einstein, but should we worry about that? So what? ... it might be that we have to learn to accept not so much AAD, but the inadequacy of no AAD.’ p.7: ‘And that is the dilemma. We are led by analysing this situation to admit that in somehow distant things are connected, or at least not disconnected. ... So the connections have to be very subtle, and I have told you all that I know about them.’ p.9: ‘It’s my feeling that all this AAD and no AAD business will go the same way [as the ether]. But someone will come up with the answer, with a reasonable way of looking at these things. If we are lucky it will be to some big new development like the theory of relativity.
Maybe someone will just point out that we were being rather silly, and it won’t lead to a big new development. But anyway, I believe the questions will be resolved.’ p.10: ‘I think somebody will find a way of saying that [relativity and QM] are compatible. For me it’s very hard to put them together, but I think somebody will put them together, and we’ll just see that my imagination was too limited.’ p.12: ‘I don’t know any conception of locality that works with QM. So I think we’re stuck with nonlocality.’ p.13: ‘... I step back from asserting that there is AAD, and I say only that you cannot get away with locality. You cannot explain things by events in their neighbourhood. But I am careful not to assert that there is AAD,’ after Bell seminar (1990)
http://www.quantumphil.org./Bell-indeterminism-and-nonlocality.pdf.
.