billschnieder said:
Are you sure? If you insist, I suppose you can provide a NON-LOCAL dataset of outcomes for three angles a, b, c which violates the inequalities. Using your assumption of non-locality, please generate such a dataset in the form:
a, b, c
-----------
-1, +1, -1
+1, -1, -1
+1, +1, -1
-1, -1, -1
-1, -1, -1
-1, +1, +1
...
For any number of photons you like. Then we will calculate the correlations from it and verify if it violates Bell's inequalities as you claim. Note you can use any assumption you like in generating the outcomes, specifically, please use non-locality and spooky action at a distance. The only condition is there are 3 outcomes for 3 angles for each photon measured.
The whole point is that such a chart has no relevance on the EPR experiment
unless we assume that there are no causal influences that travel faster than light. You have Alice choosing one of three different detector orientations, and you similarly have Bob choosing one of three different detector orientations. If you assume that Alice's result does not depend on Bob's detector orientation, and vice-versa, then that means (in a classical, realistic theory) that for run number n of the experiment, there should be probabilities
P_{n,a}, P_{n,b}, P_{n,c}, P'_{n,a}, P'_{n,b}, P'_{n,c}
where P_{n,a} is the probability, in run number n, of Alice detecting a photon at orientation a, where P'_{n,a} is the probability, in run number n, of Bob detecting a photon at orientation a, etc. You can show that there is no probability distribution on 6-tuples of real numbers that gives the quantum predictions.
But if we allow for faster-than-light causal effects, then there is no reason to assume that such 6-tuples exist. Instead, we would have an 18-tuple:
P_{n,a,a}, P_{n,b,a}, P_{n,c,a}, <br />
P_{n,a,b}, P_{n,b,b}, P_{n,c,b},<br />
P_{n,a,c}, P_{n,b,c}, P_{n,c,c},<br />
P'_{n,a,a}, P'_{n,b,a}, P'_{n,c,a}, <br />
P'_{n,a,b}, P'_{n,b,b}, P'_{n,c,b},<br />
P'_{n,a,c}, P'_{n,b,c}, P'_{n,c,c}
where P_{n,x,y} is the probability, on run n, that Alice detects a photon at angle x given that Bob's detector is oriented at angle y, and where P'_{n,x,y} is the probability, on run n, that Bodetects a photon at angle y given that Alice's detector is oriented at angle x.
There is absolutely no problem in coming up with such 18-tuples that satisfy the predictions of quantum mechanics.
The assumption of classical locality is that you can get away with just 6-tuples instead of 18-tuples.
