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johana said:Let so called "Bell test angles" be known ahead of time: 0°, 45°, 22.5° and 67.5°. How that makes it any easier to come up with a single [itex]\lambda[/itex] function that works for each combination: E(a,b), E(a,b'), E(a',b), and E(a',b')? What time has to do with any of it?
If you know the angles ahead of time, it is easy to reproduce the predicted correlations using a local hidden-variables model.
If you know ahead of time that Alice's filter is set at angle [itex]a[/itex] and Bob's filter is set at angle [itex]b[/itex], then a model that reproduces the predictions of QM is the following:
- With probability [itex]\frac{1}{2} cos^2(a-b)[/itex], send a photon to Alice that is polarized at angle [itex]a[/itex], and send a photon to Bob that is polarized at angle [itex]b[/itex].
- With probability [itex]\frac{1}{2} cos^2(a-b)[/itex], send a photon to Alice that is polarized at angle [itex]a+90^o[/itex], and send a photon to Bob that is polarized at angle [itex]b+90^o[/itex].
- With probability [itex]\frac{1}{2} sin^2(a-b)[/itex], send a photon to Alice that is polarized at angle [itex]a[/itex], and send a photon to Bob that is polarized at angle [itex]b+90^o[/itex].
- With probability [itex]\frac{1}{2} sin^2(a-b)[/itex], send a photon to Alice that is polarized at angle [itex]a+90^o[/itex], and send a photon to Bob that is polarized at angle [itex]b[/itex].
We can independently verify that if a filter is aligned in the same direction as polarized light, then it passes 100% of the time, and if it is aligned at a 90 degree angle, relative to the polarized light, then it is blocked 100% of the time.
This trivial model reproduces exactly the predictions of QM for the twin-photon EPR experiment.
It's clear that the model could not work if you don't know Alice's and Bob's filter orientations ahead of time.