In (4), if we let ##\{A(a, \lambda)A(b, \lambda)\}\{A(a, \lambda)A(c, \lambda)\}## reduce to ##A(b, \lambda)A(c, \lambda)## by allowing ##A(a, \lambda)A(a, \lambda)=1,## (as stated) then the integral gives ##-E(b,c) ##. It is similar to the way you get the same final result.
You and I and Bell...
For PeterDonis: Of course! Many thanks and my apologies! The problem occurs lower down! Let me redefine it using {.} to keep related terms together:
From the first eqn in Post #51 above, including the integrals in line with Bell (1964):
$$E(a,b)-E(a,c)=-\smallint d\lambda...
From the second eqn in Post #51 above, completing the integral in line with Bell (1964):
$$\smallint d\lambda \rho(\lambda)A(a, \lambda)\left[A(c, \lambda) - A(b, \lambda)\right]=0$$
since ##A(a, \lambda)## is a function of ##\lambda## and takes the values ±1 randomly.
Are you in a position to help me find my error?
It looks like a straight-forward integral whose first term (a function of λ) takes the values ±1 randomly?
Please, I am not seeking to refuse anything. I am seeking to understand what I am being told. I understood you to say that Bell's inequality is based on mathematics unrelated to QM.
In asking me to show my work in detail: by observation it appears that completion of the integral over DarMM's...
But can't we test your basic algebra by stopping at the second equation and completing the integral there?
Since the result is nothing like Bell's inequality, it looks like Bell's difficulties are already in the second equation?
Sorry for my slowness; I share your frustration. Did you reply to post #15. That will help me to see how Bell's mathematical model departs from QM and nature. Thanks.
OK, thanks, let me try again. Let's call the 2 top equations on p.198: (14a) and (14b).
So, to me, (14a) is true; it is simply a definition of Bell's terms.
But (14b) looks false to me; and this view is backed by the fact that it (by plain mathematics) leads to Bell's famous eqn (15): which IS...
Yes to (X) and the difference between the first and second integral on p.198. But I think (Y) is invalid.
To be clearer: I am seeking to understand the "physics" that Bell has in mind when using his eqn (1) to move from the 2 instances in p.198's first eqn to the 2 instances in p.198's second...
Thank you. I like this approach, and appreciate you taking such a clear position. Especially as it seems to me that realism [a term to me so confusedly used] "of some sort" gives rise to this question:
Could you explain please (in your terms) "the physics" (shall we call it) behind Bell's move...
But aren't the Bell inequalities based on naive-realism?
By which I mean views like this:
I ask because [if true] such would appear (to me) to be so naive as to be dismissed out of hand? And to thus have no relevance to locality?
PS: What is your definition, please, of the realism that...
Many thanks for this helpful detail.
I would like to be consistent with relativistic QM and microcausality. So it seems to me that "signal locality" would be bound by Einstein-locality : more clearly defined as "No beable propagates superluminally".
Then, it seems to me and I would hope...