CH Inequality

[FrediFizzx]

So... since we have learned that since the probability terms in the CH inequality can only range from 0 to 1/2 because it only deals with + and ++ counts, then I believe the CHSH probability version based on CH would be the following.

|p(a, b) - p(a, b') + p(a', b) + p(a', b')| ≤ 1

Remembering that we are only dealing with ++ counts for each term. So we could have for independent terms,

1/2 - 0 + 1/2 + 1/2 = 1.5

So 1.5 is the absolute bound for independent terms of this version. Another thing is that an experimenter would have to know N the total number of emissions for each term. So this version is not reallly practical as far as experiments go.

[FrediFizzx]

Yeah, I guess minkwe, that basically started this thread, got busy for the holidays. And I guess Joy doesn't care about the CH inequality. Anyways I think our discussion bore some fruit. I finally figured out that the maximum result of QM for the CH74 string is about 0.207. According to Ballentine in "Quantum Mechanics: A Modern Development", P1 = P2 = 1/2 and P12(θ) = (cos(θ)^2)/2 and the CH74 string can be expressed as,

3*P12(θ) - P12(3*θ) - P1 - P2

According to Ballentine a maximum result occurs at 22.5 degrees which I think is for a photon state so plugging in the values we get,

1.28 - 0.073 - 1 = 0.207

So I think this confirms my result of the independent absolute bound of CH being 1/2. We could have for independent terms,

1/2 - 0 + 1/2 +1/2 - 1/2 -1/2 = 1/2

Yeah, finally!!!!!!!!
****

So the CH ratio for independent terms becomes,

(1/2 - 0 + 1/2 + 1/2)/(1/2 + 1/2) = 1.5

Then using independent terms, like they do in experiments and QM, a valid violation would have to exceed 1.5. Of course "valid violation" is an oxymoron as I pointed out in another thread since it is mathematically impossible to violate an inequality.

[minkwe]

"Even though we have introduced λ as the state of a specific single system, the assumed objectivity of the system described by this state allows us to consider an ensemble of these, physically identical to the extent that they are all characterized by the same λ. The probabilities are to be associated with this ensemble. Clearly, this procedure is conceptually sound, even in cases where we cannot in practice prepare the pure λ ensemble," CH74, p.534, footnote 11 (with my underlining).

I'd welcome any and all comments on this footnote; even to the point of suggesting a new thread: "Bell's first error revealed!" But that would be conditional on a few others seeing the gross boo-boo and oops in the cited footnote!

My thanks again; Gordon

Yes, I had spotted the same. Even so, there are still many people with heads in sand claiming the CH inequality makes no such assumption.