Ed. Your penultimate post is pasted here, my replies inserted. I'll do the same, in a new post, with your last post. NB: I'm now attempting to practice precision; putting a temporary halt to our easy (yet understandable) colloquialisms. Alas, I'm sure to sin; which I'm thinking is maybe OK: For you're sure to improve things in review; as is your custom.
EK: = ""Gordon, You were correct that my terminology confused particles and settings. Now you state:
"The error occurs as you say: when he tries to use a factor of +1 in (14 a)."
Please confirm that you mean: "Bell's error occurs as I say..."
not "I make an error when I say..." ..""
GW: Ed (EK) is correct when he says that Bell's errors begin as Bell moves from his (14a) to (14b).
EK: = ""Then you say "but your notation and reasoning is not quite correct." I believe my notation is correct, but inconsistent with yours. And I should have followed through, so I would say my reasoning, as presented, is incomplete. As you note, it is when he does this insertion that the error pops up between A(a,Li) and A(c,Ln+i), [where I am now using 'L' for 'lambda', as was done in comments on Joy's blogs]. And it is not just because he cannot guarantee the result is +1, but because of what results after the insertion.""
GW: I agree with your last sentence, but it is now out-of-order - "insertion" in BT contexts now banned! So:
In the interest of total precision, let's make Bell's (14a) physically significant. Let's represent the (signed) core [.] of his integral in (14a) as follows:
- [A(a,L1)A(b,L1) - A(a,L2)A(c,L2)]. ---(14a*)
Where the numbered Ls (= lambdas; L1 and L2) come from odd and even numbered particle-pairs respectively; ie, we do NOT follow the Essay and run n AB tests over particle-pairs 1-n; then run n AC tests over particle-pairs (n+1)-2n.
INSTEAD we do one AB test with particle-pair#1; then one AC test with particle-pair#2; then one AB test with particle-pair#3; etc.
So we have, with precision:
(14a*) = A(a,L1)A(b,L1)[A(a,L1)A(b,L1)A(a,L2)A(c,L2) - 1]. ---(14b*)
Now the core of our (14b*) here should equal the core [.] of Bell's (14b). That is:
(14b**) = [A(a,L1)A(b,L1)A(a,L2)A(c,L2) - 1] =?= [A(b,L?)A(c,L?) - 1]. ---(14b)
NB: L? is in play here because we have (as yet) few clues as to what Bell's up to.
But A(c,L?) must be A(c,L2) because setting L2 was only ever tested against 'c'.
And so A(b,L?) must be A(b,L2)!
BUT setting L2 was NEVER tested against 'b' -- so here's nonsense and Bell's 1st impossibility.
WITH equally no escape in reverting to P(b,c) = A(b,L1)A(c,L1); since L1 was never tested against 'c'.
It's crazy!
YET: Via his introduction to his (15), Bell agrees that A(b,L?)A(c,L?) = P(b,c) in (14c); and so too in his (14b). So is it somehow possible to remove the =? from between our (14b**) and Bell's (14b) above? Can you and I agree with Bell; for all that we each require is:
A(a,L1)A(b,L1)A(a,L2)A(c,L2) = crazy A(b,L2)A(c,L2) or crazy A(b,L1)A(c,L1); that is
A(a,L1)A(b,L1)A(a,L2) = A(b,L2); or A(a,L1)A(a,L2)A(c,L2) = A(c,L1)---(X)
Alas: You and I know IMPOSSIBLEs when we see them; Bell and his supporters do not. For, inadvertently requiring AND allowing the IMPOSSIBLE L1 = L2, they make the nonsense in (X) the norm. QED!
EK: = ""My notation was inconsistent because your readers may still be confused by the i and n+i and I wanted to show that in general A(x,L) A(x,L') won't be equivalent to +1 for any setting x but different parameters (L, L') if L and L' characterize different runs.""
GW: Sir, you trespass here on hallowed ground. That prime (') has been my little mate since day-one. So me, seeing A(x,L)A(x,L'), knows that it is ALWAYS -1.
However, your thoughts so pure and well-intentioned, can we use "something like" that L1 and L2 that have served us so well above? (PS: But I'd like it to be close to the Essay.)
NB: I'm a stickler for developing friendly intuitive natural efficient notations; one beautiful notation for all.
EK: = ""And I left the details incomplete because my next comments were to discuss the fact that Bell has four A's but you have six A's, and this is the area where his problem shows up. I felt it was too much detail for one comment.""
GW: Check and see if you'd be happy with Bell's four. (I suspect not; though it would be good to match Bell at every step.) I'm pretty sure that I need six to ensure absolute precision, beyond reproach (as above).
EK: = ""I'm usually not such a stickler for words, but I know from Joy's experience that 1.) every word counts, and 2.) every word must be correct.
Thank you for pointing out the link to Bell's paper in your references. I've been using "Unspeakable..." [pages 14 to 19] but many do not have that book.
As I noted, I do not normally make such a fuss over words, but this "disproof" has got to be perfectly correct. After we beat these points into the ground I plan to clean up the above notes, with both your equations and Bell's equations in proper format, but only after all "incorrect" or "incomplete" reasoning has been straightened out. My final writeup will not have all of these if's, and's, and but's.""
GW: You have my full support in these endeavours.
With best regards; Gordon. E and OE! 1 post to follow: #