- 8,400

- 2,573

I have no idea what you are talking about. What it boils down to is that there is a joint probability distribution for Alice and Bob: [itex]P(\alpha, \beta) = \frac{1}{2} sin^2(\frac{1}{2} (\beta - \alpha))[/itex]. This joint probability distribution gives rise to a particular correlation between Bob's measurements and Alice's measurements. This correlation can be tested experimentally, and the prediction is born out. So experiment confirms the predictions of quantum mechanics.If such a dataset is impossible then what dataset is being used to compare experiments to the inequalities, or are you now claiming that the experiments do not produce datasets?

What Bell showed is that you can't simulate the joint probability distribution [itex]P(\alpha, \beta)[/itex] by a "factored" distribution of the form

[itex]\int d\lambda P_A(\alpha, \lambda) P_B(\beta, \lambda) P_L(\lambda)[/itex]

Bell's inequality gives a bound on the greatest correlation that can be simulated by "factored" probabilities of this form.

The dataset you are asking for is

*NOT*what is measured in experiments. We already know ahead of time that there is no such dataset, so there's no point in testing that. What is measured in experimental is the correlations between Alice's and Bob's measurements.