You want to talk about a different paper instead, which BTW I already demolished here

viewtopic.php?f=6&t=6&start=20I have pointed out the logical fallacies in your point of view already and I will summarize it below for anyone who is interested. See this posts for example:

viewtopic.php?f=6&t=23&start=30#p651. I'm not expecting a coherent response to any of these points, having given you plenty of opportunity to address the inconsistency in vain:

1) In your LG paper, you admit that the CHSH and Bell inequalities are only valid if the same ensemble is used to calculate every correlation:

Larsson & Gill wrote:The problem here is that the ensemble on which the correlations are evaluated changes with the settings, while the original Bell inequality requires that they stay the same.

2) In your paper, you admit that when 4 different ensembles are being used the inequalities therefore only applies to the common part of the 4 different ensembles:

Larsson & Gill wrote: In eﬀect,the Bell inequality only holds on the common part of the four diﬀerent ensembles

3) In your LG paper, you attempt to rescue the CHSH for four different ensembles and, you admit that the CHSH can be saved ONLY if the common part is a non-null set,

Larsson & Gill wrote:Theorem 2 (The CHSH inequality with coincidence restriction), The prerequisites (i–iii) of Theorem 1 are assumed to [u]hold except at a null set[/u]

...

The proof consists of two steps; the first part is similar to the proof of Theorem 1, using the intersection

ΛI= ΛAC′ ∩ ΛAD′ ∩ ΛBC′ ∩ Λ BD′

...

This ensemble may be empty, but only when δ = 0 and then the inequality is trivial, so δ >0 can be assumed in the rest of the proof

4) In your paper, relying on the assumption that the common part of the 4 different ensembles is not a null set, and δ >0, you derive a new inequalities below, where γ is the probability of coincidence (aside: somebody should ask Richard what the inequality is for 50% coincidence efficiency, γ=0.5, according to his LG paper).

Larsson & Gill wrote:We now have

δ ≥ 4 − 3/γ

...

Putting this into our modified CHSH inequality we arrive at

| E(AC′|ΛAC′) + E(AD′|ΛAD′)| + |E(BC′|ΛBC′) − E(BD′|ΛBD′)|≤ 6/γ − 4

5) Clearly, your above inequalities are not valid if δ = 0. Which means your new inequality is not valid if there is no common part of the 4 different ensembles.

6) You admit in your other paper that in EPR experiments, the correlations are calculated from 4 different ensembles of particles.

Gill wrote:In each run, Alice and Bob are each sent one of a new pair of particles in the singlet state. While their particles are en route to them, they each toss a fair coin in order to choose one of their two measurement directions. In total 4N times, Alice observes either A = 1 or A' = 1 say, and Bob observes either B = 1 or B' = 1. At the end of the experiment, four "correlations" are calculated; these are simply the four sample means of the products AB, AB', A'B and A'B'. Each correlation is based on a different subset, of expected size N runs, and determined by the 8N fair coin tosses.

7) You admit when I specifically asked you, that indeed the 4 ensembles in the EPR experiments are disjoint:

gill1109 wrote:minkwe wrote:... do you deny the fact that the sets of particles used to measure each correlation are disjoint?

Answer: No.

8) Yet you continue to believe that experiments, measure and calculate correlations from 4 disjoint ensembles have confirmed Bell's theorem, which relies on an inequality using a single ensemble of particles.

9) Yet you continue to believe that QM, which makes predictions for 4 disjoint ensembles particles, violates the CHSH which is derived from a single ensemble of particles.

10) Yet you claim not to understand when I say:

the apparent violation of the CHSH by QM and experiment is only due to the error of substituting actual results from 4 disjoint ensembles into an inequality which expects counterfactual results from a single ensemble. In fact you make the jaw-dropping claim that:

gill1109 wrote:minkwe wrote:"We can not substitute actual outcomes from a different set of particles for counterfactual outcomes of a single set of particles."

Nobody is doing that. There is a substitution of theoretical mean values by empirically observed averages.

11) Forgetting that you have already admitted already that the theoretical mean values are obtained from the same ensemble of particles, while the empirically observed averages are obtained from 4 disjoint ensembles of particles.

12) You continue to believe that statistics, or probability or fair sampling, or random sampling can cause the 4 disjoint ensembles in Bell-test experiments to impart constraints on each other such that the

upper bound of the expression based on 4 disjoint ensembles of particles {1}, {2}, {3} and {4}:

<a1b1> + <a2b2′> + <a3′b3′> − <a4′b4>

is reduced below 4.